hi!!! i’d appreciate it sm if someone could do 25 and 26 i’m thing to turn my work in tomorrow and these are the last ones i need, i’ll mark u brainliest when it pops up :) thank you
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]
Related Questions
what is the value of x
Answers
The value of x is [tex]x=\frac{268}{3}[/tex] = 89.33 degree.
How do you find value of x?
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values. The letter "x" is frequently used in mathematics to denote an unknowable amount or variable. Similar to how X-rays confounded their discoverer and Malcolm X adopted the sign to stand for the lost name of his African ancestry, x also denotes the unknown in English.
x+44+x+3+x+45=360
Group like terms
x+x+x+44+3+45=360
Add similar elements: x+x+x=3 x
3 x+44+3+45=360
Add the numbers: 44+3+45=92
3 x+92=360
Move 92 to the right side
3 x=268
Divide both sides by 3
[tex]\frac{3 x}{3}=\frac{268}{3}[/tex]
Simplify
[tex]x=\frac{268}{3}[/tex]
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he table of values represents a quadratic function f(x).
x f(x)
−7 14
−6 7
−5 2
−4 −1
−3 −2
−2 −1
−1 2
0 7
1 14
What is the equation of f(x)?
f(x) = (x − 4)2 − 1
f(x) = (x − 3)2 − 2
f(x) = (x + 3)2 − 2
f(x) = (x + 4)2 − 1
Answers
The equation of the quadratic function is (c) f(x) = a(x + 3)² - 2
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (-3, -2)
Substitute (h, k) = (-3, -2) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x + 3)² - 2
Also, from the graph, we have the point (0, 7)
This means that
a(0 + 3)² - 2 = 7
So, we have
9a = 9
Divide both sides by 9
a = 1
Substitute a = 1 in f(x) = a(x + 3)² - 2
f(x) = a(x + 3)² - 2
Hence, the equation is f(x) = a(x + 3)² - 2
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Answer:
hey um im back....
Step-by-step explanation: i was in the ER from being abused and you did not lose me don't worry i love you i was moving place to place so i did not have my phone i wish i could undo this all but im ok now love
michelle
The time spent by a customer at a checkout counter has mean 4 minutes and standard deviation 2 minutes.
a. What is the probability that the total time taken by a random sample of 52 customers is less than 180 minutes?
b. Find the 30th percentile of the total time taken by 52 customers.
Answers
The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.
μ=Population mean=4
σ=Population standard deviation=2
n=Sample size=50
The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.
The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.
The sum S's sample distribution has a mean and standard deviation of n and n, respectively.
The z-score is the value decreased by the mean, divided by the standard deviation
z = ( x -μS ) / √σS
= 150 - 50(4) / √ 50(2)
= 3.54
Using the appendix's normal probability table, get the relevant probability,
P(S < 150 ) = P(Z< -3.54)
= 0.0002
=0.02%
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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The length of a rectangle is twice the width. The area of the rectangle is 80 square inches. What irrational number represents the width of the rectangle?
Answers
The square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.
What is a rectangle?
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral. It occupies area in two-dimensional planner geometry.
The area of a rectangle is given by the formula A = lw,
where A is the area, l is the length, and w is the width.
We are told that the length of the rectangle is twice the width, so we can write the formula as follows:
A = 2w * w
We are also told that the area of the rectangle is 80 square inches, so we can substitute this value into the formula:
80 = 2w * w
We can rearrange this equation to solve for w:
80 = 2w²
w² = 40
The square root of 40 is an irrational number, so the width of the rectangle is an irrational number.
Hence, To express this number in decimal form, the square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.
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Profit margin ratio 294\3800
Answers
Step-by-step explanation:
12.93 is the answer of this question.
Consider the interval AC that has been graphed on the number plane. Find the length of interval AC, rounding your answer to two decimal places.
Answers
By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.
What is the distance formula?The distance formula is given as:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Give the example of two decimal rounding off.
Here are two examples of rounding off to two decimal places:
12.3456 rounded to two decimal places is 12.35
0.678 rounded to two decimal places is 0.68
Plugging in the coordinates of the two points, we get:
Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)
= sqrt(6^2 + (-9)^2)
= sqrt(36 + 81)
= sqrt(117)
= approximately 10.8
Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.
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the values f(x) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1. which of the following statements must be true?
Answers
The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
Given :
the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.
Function :
In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and a co - domain.
x sufficiently close to 1 means x → 1
but x ≠ 1.
so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞
Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
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In a certain chemical, the ratio of zinc to copper is 4 to 17 . A jar of the chemical contains 561 of copper. How many grams of zinc does it contain?
Answers
Answer:
7,293 if I am correct.
Hope this helps!
If a snowball melts so that its surface area decreases at a rate of 4 cm²/min, find the rate at which the diameter
decreases when the diameter is 39 cm.
Answers
The surface area of a snowball can be represented by the formula:
A = 4πr^2
where A is the surface area, r is the radius of the snowball, and π is a constant approximately equal to 3.14.
If the surface area of the snowball decreases at a rate of 4 cm²/min, we can represent this as a derivative:
dA/dt = -4
where dA/dt is the rate of change of the surface area with respect to time, and t is the time in minutes.
The radius of the snowball is equal to half the diameter, so we can represent the radius as:
r = d/2
where d is the diameter of the snowball.
Substituting this expression for r into the formula for the surface area and differentiating with respect to time, we get:
dA/dt = 8π(d/2)dr/dt
Setting this expression equal to -4 and solving for dr/dt, we get:
dr/dt = -4 / (8π)
= -0.5 / π
When the diameter of the snowball is 39 cm, the rate at which the diameter decreases is:
dr/dt = -0.5 / π
= -0.15915494309189533576888376337251
Therefore, the rate at which the diameter of the snowball decreases when the diameter is 39 cm is approximately -0.159 cm/min.
I hope this helps
Solve for a given the following proportion:
4/a-3=2/5
a=
Answers
Answer:
first do criss cross the it will be like this : 2(a-3)=4*5 . Now do like as given in the picture.
what is the answer to this 6m+8=4(17+m)
Answers
Answer:
m=30
Step-by-step explanation:
*Triangle not drawn to scale*
- Which angle is the biggest based on the sides of the triangles below? Explain your reasoning.
Answers
Using Triangle inequality theorem Angle C of triangle CBT will be the biggest angle.
What do you mean by triangle inequality?Triangle inequality. A theorem in Euclidean geometry that states that the sum of any two sides of a triangle is greater than or equal to the third side. In symbol a + b ≥ c. Basically, the theorem states that the shortest distance between two points is a straight line.
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides of it must be greater than or equal to the length of the remaining sides.
In the given triangle CBT , CB = 24 cm BT = 35 cm CT = 30 cm
We know angle opposite to larger side will be greatest therefore, angle C of triangle CBT will be the biggest angle
.
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Consider r (x) = StartFraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline EndFraction, where a, b, c, and d are positive integers and b < d. What value does r(x) approach as x approachesInfinity?
0
StartFraction a Over c EndFraction
StartFraction b Over d EndFraction
Infinity
Answers
The value of r(x) approaches as x approaches Infinity is; 0
How to find the limit of a function?Limit is defined as the value that a function approaches for the given input value.
We have been given a function;
r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction
We can rewrite this function as;
r(x) = (axᵇ + 8)/(cx^d)
where a, b, c, and d are positive integers and b < d.
We need to find the value of r(x) approach as x approaches Infinity.
This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]
Now, we find the value of limit for given function;
[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]
This simplifies to;
[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)
Thus;
[tex]\lim_{x \to \infty} r(x) = 0[/tex]
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Box contains 160 fruits. of the total number of fruits in the box 30% are apples. 25% of the remaining fruits in the box pears and the rest of the fruits in the box are oranges. how many oranges are in the box?
Answers
Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.
Therefore, in area or a circles given by the formula.
A. the circumference, or 2π²
B. the radius, r
C. half the radius, or 1/2 r
D. half the circumference, or s r
Answers
Area or a circles given by the formula = radius , r
What is area?
The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
For the circle or area given by the formula is radius ,r.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
USE EFFICIENT METHODS Determine whether Δ D E F P ≅ ΔP Q R.
D(-7,-3), E(-4,-1), F(-2,-5), P(2,-2), Q(5,-4), R(0,-5)
Find the side lengths of each triangle.
A) D E=√13, P Q=√13, E F=2 √5, Q R=√13, D F=√29, P R=√13
B) D E=√13, P Q=√13, E F=√5, Q R=√26, D F=√29, P R=√13
C) D E=√13, P Q=√13}, E F=2 √5, Q R=√26, D F=2 √29, P R=√13
D) D E=√13}, P Q=√13, E F=2 √5, Q R=√26, D F=√29, P R=√13
Answers
The side lengths of each triangle are given as follows:
D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]
How to obtain the side lengths of each triangle?The side lengths of each triangle are given by the distances between the vertices.
These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.
Suppose two points in the coordinate plane with notation given as follows:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Then the distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus the side lengths are given as follows:
DE: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]PQ: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]EF: [tex]\sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}[/tex]QR: [tex]\sqrt{5^2 + 1^2} = \sqrt{26}[/tex]DF: [tex]\sqrt{5^2 + 2^2} = \sqrt{29}[/tex]PR: [tex]\sqrt{2^2 + 3^2} = sqrt{13}[/tex]Meaning that option D is correct.
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Jared draws a rectangle. Explain how
to find the area using the Distributive
9 ft length
5 ft height
Answers
45 feet is the answer
During the school fundraiser 4/6 of the products sold were flavored popcorn. Of the flavored popcorn, 1/2 who was caramel flavored. What fraction of the fundraiser products is caramel flavored popcorn?
Answers
Answer:
3/10
Step-by-step explanation:
please mark me brainliest if this is right
A consulting company wants to track the results of its new marketing plan. The media manager recorded the number of views for one of the company’s online videos. The results from the first four weeks are shown in this table.
Write an equation to model the relationship between the number of weeks, x, and then number of views, f(x).
f(x)=a(b)^x
Answers
The equation which model the relationship between the weeks and the viewers is;
f(x) = 2160(1.5)ˣ
What is common ratio?The distance between each number in a geometric series is known as the common ratio. The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.
Given that the expression f(x) = abˣ
Here, b is the common ratio.
Now to find the common ratio b;
To check for first and second term, 3240 / 2160 = 1.5
To check for second term and third term, 4860 / 3240 = 1.5
To check for third term and forth term, 7290 / 4860 = 1.5
To check for forth and fifth term, 10935 / 7290 = 1.5
Therefore the common ratio b is 1.5.
now to find a,
let x =0 and f(x) = 2160
Then, 2160 = a (1.5)°
a = 2160
Therefore, the equation which model the relationship between the weeks and the viewers is;
f(x) = 2160(1.5)ˣ
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An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
Answers
well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25[/tex]
Graph the line with -intercept -4 and slope 6
Can you mark the points
Answers
The graph of the given line with y-intercept -4 and slope 6 is given below.
What is slope intercept form?
One of the most popular ways to represent the equation of a line is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
For a straight line with slope "m" and y-intercept "b," the slope-intercept form equation is:
y = mx + b.
Given, y-intercept (b) = -4
slope (m) = 6
Then, the equation of the graph will be
y = 6x - 4
The graph of the equation with points is given below:
Hence, this is the required graph of the slope-intercept form line.
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help please easy math proportional relationships, due now please help needed
Answers
By knowing that the cost equation must be a proportional relation, we will find that the equation is:
y = $0.64*x
Which equation can be used to find the cost of x pounds?
The cost equation is proportional, if we define y as the cost and x as the number of pounds, the equation is something like:
y = k*x
We know that for (5 + 1/2) pounds the cost is $3.52, then we can replace these values in the equation above to get.
$3.52 = k*(5 + 1/2)
$3.52/(5 + 1/2) = k = $0.64
Then the cost equation for x pounds of potatoes is:
y = $0.64*x
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Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon
Answers
The cost of driving Jenna's car is $0.341/mile
Calculating cost of drivingFrom the question, we are to determine the cost of driving Jenna's car in $/mile
From the given information
The formula used to find Jenna's cost to drive her own car for work is
J = g/22 + 0.146
We are to find the cost of driving when the price of gas, g, is $4.29/gallon
Substitute g = 4.29 in the formula
J = 4.29/22 + 0.146
J = 0.195 + 0.146
J = 0.341
Hence, the cost is $0.341
Here is the complete question:
Recall the formula used to find Jenna's cost to drive her own car for work:
J = g/22 + 0.146
In this formula, J = Cost of driving Jenna's car in $/mile, and g = Cost of gas in $/gallon.
Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon
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What inverse trig function would be used to solve for angle Z?
Answers
The inverse sine trig function would be used to solve for angle Z .
What is meant by inverse sine ?In the right angle triangle the ratio of the opposite to the hypotenuse of any acute <A is called the sine of < A
The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal. It produces the angle's value.
The opposite of the sine function is the inverse sine function, also known as arcsine. Due to the fact that the sine of an angle (or sine function) is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of this ratio will provide the angle's measurement.
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5. Determine the coordinates of point Y so that JY = (2/3)JK.
Answers
The coordinates of y so that JY = (2/3)JK is Y = 2/3k
What are coordinates?Coordinates are a pair of numbers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.
The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical)
How to find the coordinates of YExamining the expression given JY = (2/3)JK, it can be seen that
at the left part of the equation Y is present while at the second part of the equation Y is no replaced by 2/3k
Hence the 2/3k is equal to Y, and this represents the points that defines Y
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A local bank charges a $31-per-check overdraft protection fee. On June 5, Lewis has $932.77 in his account. Over
the next few days, the following checks were submitted: June 6, $791.29, $340.50, and $208.35; June 7, $428.61;
and June 8, $113.3. How much will he pay in overdraft fees?
Answers
Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.
Step-by-step explanation:
To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:
overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)
= 932.77 - 2082.05
= -1149.28
Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.
Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.
The populations of 2 cities grow according to the exponential functions. Pi(t) = 120 e 0.011 t P2(t)= 125 e 0.007 t Where, P₁ and P2 are the populations (in thousands) of cities A and B respectively. t is the time in years such that t is positive and t = 0 corresponds to the year 2004. When were the populations of the two cities equal and what were their populations?
Answers
Hello,
I hope you and your family are doing well!
To find when the populations of the two cities are equal, we can set P1(t) = P2(t) and solve for t:
120 e 0.011 t = 125 e 0.007 t
Dividing both sides by e 0.007 t:
120 = 125 * (e 0.011 t / e 0.007 t)
Using the property that e^(a+b) = e^a * e^b, we have:
120 = 125 * e^(0.011 t - 0.007 t)
120 = 125 * e^(0.004 t)
Dividing both sides by 125:
1.2 = e^(0.004 t)
Taking the natural logarithm of both sides:
ln 1.2 = ln e^(0.004 t)
ln 1.2 = 0.004 t
t = ln 1.2 / 0.004
t = approximately 8.44 years
Therefore, the populations of the two cities were equal approximately 8.44 years after 2004, or in the year 2012. To find the population of the two cities at this point in time, we can substitute t = 8.44 into either of the exponential functions:
P1(8.44) = 120 e 0.011 * 8.44 = approximately 123.88 thousand
P2(8.44) = 125 e 0.007 * 8.44 = approximately 123.88 thousand
Therefore, the populations of the two cities were equal to approximately 123.88 thousand when they were equal.
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The function f(x)=(−x+4)(2x+2) is written in factored form.
Drag statements into the table to show what each factor tells you about the graph of the function. Imagine math
Answers
The intersection of the curve with the x-axis will be at (−1, 0) and (4, 0) for each factor.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function written in factored form is given below.
f(x) = (−x + 4) (2x + 2)
For the factor (−x + 4), we have
−x + 4 = 0
x = 4
For the factor (2x + 2), we have
2x + 2 = 0
2x = −2
x = −1
The intersection of the curve with the x-axis will be at (−1, 0) and (4, 0) for each factor.
The graph is given below.
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Adrian Alvarez Munoz
Write Expression from Context $(m x+ b)
Dec 12, 8:15:06 PM
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Angel is saving up to buy a new video game. He already has $ 30 and can save an additional $ 8 per week using money from his after school job. How much total money would Angel have after 5 weeks of saving? Also, write an expression that represents the amount of money Angel would have saved in w weeks.
Total savings after 5 weeks:
Total savings after w weeks:
Answers
The expression that represents the amount of money Angel would have savings in w weeks is 30+8w
The total amount of money saved after 5 weeks is $70
Which algebraic expression is required for Angel's total savings?
The required algebraic expression considers the amount she has saved already which is $30 and her potential to save $8 per week, for w number of weeksSystems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Total savings=30+8w
Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks
total savings=30+(8*5)
total savings=30+40
Total savings=$70
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Consider the following statement: Let f be a function, such that for all a and b in the domain of f, f(a)=f(b) implies a=b. Then the function f has an inverse. Is this statement true or false?
Answers
True, the given function f has an inverse.
A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. Inverse functions f and g result in f(x) = y if and only if g(y) = x.
Under the given condition, we can define the function g on the set of the images {b | b = f(a), a belongs to A} in a way
g(b) = a, if f(a) = b.
This function is defined correctly on this set and is the inverse function to f.
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