What is inverse of the function f(x) = 4(x - 3)?

Answers

Answer 1

The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.

What is meant by inverse function?

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.

Let f(x)=y

f(x)=4(x-3)

f(x)=y

y=4(x-3)

x=4(y-3)

x=4y-12

4y=x+12

y=(x+12)/4

Therefore, f⁻¹(x)=(x+12)/4

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Related Questions

Please ignore the triangles on the side

best answer gets brainliest

Answers

Answer:

103.98cm

Step-by-step explanation:

14 + 14 = 28

20 + 20 = 40

(14(3.14)) / 2+ 14 = 35.98cm

40 + 28 + 35.98 = 103.98cm

PLEASE HELP ASAP! (35 POINTS)

Ummi sees an advertisement for her favorite cereal. Then she writes these quotients.

2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1

Part A: What do Ummi's quotients represent in this situation?

Part B: If you were to graph the (weight, cost) pairs for each box, would you be able to draw a straight line through the points? EXPLAIN.

ANSWER ALL PARTS.

Answers

Ummi's quotients in this situation represent the unit rates of the advertisement

You will not be able to draw a straight line through the points

Part A: What do the quotients represent?

From the question, we have the following quotients parameters that can be used in our computation:

2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1

These can be rewritten as

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The quotients mean that

Unit rate = Total amount spent/Number of adverts

So, the quotient expressions represent the unit rate

Part B: Would you be able to draw a straight line through the points?

Recall that

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The values of the quotients are not equal

This means that it is not possible to draw a straight line through the points

Answers

12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:

y = 2x

x - y = 10

13: Just find two lines that cross (6, -4).

You can use point-slope form:

y - y1 = m(x-x1)

y + 4 = m(x - 6)

then choose two equations with different m's

y = 2(x-6) - 4

y = 3(x-6) - 4

14:

Line one has a slope of two and an intercept at y=0 so it is y = 2x

Line two has a slope of one and an intercept at y=-1 so it is y = x - 1

To find the solution of the system, substitute y:

2x = x - 1

x = -1

Then plug back in:

y = 2 * -1 = -2

So the solution is: (-1, -2)

Which value for x makes the sentence true? 4x - 2 = 18 A. x = 5 B. x = 4 C. x = 24 D. x = 20

Answers

Answer: X = 5

Step-by-step explanation:

4x - 2 = 18

+2 +2

4x = 20

/4 /4

x = 5

4(5) -2 =18

20 - 2 =18

18=18

what is the probability of drawing two aces from a standard deck of cards, given that the first card is an ace? the cards are not returned to the deck.

Answers

1/34 is the probability of cards are not returned to the deck.

What does the math term "probability" mean?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

Statistics is the study of events subject to probability.

A = the first card of ace.

B = Drawing two ace from a standard deck

P(AB) = ²C₄ / ²C₃₂

P(A) = ¹C₄ ¹C₅₁ / ²C₃₂

P(B/A) =P(AB)/P(A)

= ²C₄ / ²C₃₂ * ²C₃₂ / ¹C₄ ¹C₅₁

= ²C₄ /¹C₄ ¹C₅₁

= 1/2 * 17

= 1/34

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Solve the following problems

Answers

The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

What is Thales theorem?

Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given are three figures of triangles,

Figure 1)

5/x+5 = 8/10

50 = 40+8x

x = 5/4

y = 7/7+y = 8/10

70 = 56 +8y

y = 4/7

Figure 2)

12/12+y = 18/18+6

12/12+y = 18/24

48 = 36 +3y

y = 4

12/4 = x/5

x = 15

Figure 3)

y/4 = 1.5/3

y = 2

x/6 = 1.5/3

x = 3

Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

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Gia is making chocolate truffles. Using the table, find the constant of proportionality

Answers

Using the table we find the constant of proportionality is 15/8

What is constant of proportionality?

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.

Here,

Since from the table we have to find the constant of proportionality

So, the values of ounces of milk(x) are

30,45

and the values of amount of truffle(y) are

16,24

So for finding the constant of proportionality We take 2 cases,

a)Taking first values of x & y

x/y=30/16

x/y=15/8

b)Taking secondary values of x & y

x/y=45/24

x/y=15/8

Therefore the constant of proportionality is 15/8

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What is the result of -21÷(-2-5)+(-14)+6×(8-4×3) ? I need help

Answers

Combined calculation:

Answer:

[tex]\begin{gathered} \sf - 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 4 \times 3) = \\\sf- 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 12) = \\ \sf- 21 \div( - 3) + ( - 14) + 6 \times ( - 4) = \\ 7 + ( - 14) +( - 24) = \\ \sf 7 - 14 - 24 = \\ \sf - 7 - 24 = \\ \sf \green{ - 31}\end{gathered}[/tex]

When we solve combined calculations, we must first separate into terms when there is an addition or a subtraction.

Then, we solve the operations respecting the hierarchical order of the operations:

First we solve the powers and roots.Then divisions and multiplications.Finally, addition and subtraction.

If the calculation has grouping signs, they must be solved in the following order:

Parenthesis.Brackets.Keys.

Merry Christmas and Happy New Year

The Alpha.

Answer:

negative 36

Step-by-step explanation:

You will useva method known as BODMAS its a principle of combined operations like the one above in mathematics.

B-brackets

O-Of (multipliction) ;commonly used when fractions are involved

D- division

M- multiplication

A- addition

S- subtraction

Working out:

first we will solve the brackets then rewrite the question with the answer obtained

-2-5=-7

8-4×3= minus 4

new question :

-21÷-7+-14+6×minus 4

Next is division since there is no of

-21÷-7=3

Negative divided by negative equals positive

3+minus 14 +6×minus 4

Now do multiplication 6×minus 4= minus24

3+ minus 14+minus 24=minus 36

For the function f(x) = 2x +8, determine f(-3)
A) 2
B) 3

Answers

Answer:

Step-by-step explanation:

we replace x with -3

f(-3)=2(-3)+8

f(-3)=-6+8

f(-3)=2

hopes this helps please mark brainliest

2 1/2 + 3 1/5 x 5 5/8

Answers

The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2

What is Fraction?

fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction

2 1/2 = 5/2

3 1/5 = 16/5

5 5/8 = 45/8

which reduces it to

5/2 + 45/8 x 16/5

using BODMAS we taking care of the multiplication section first

45/8 x 16/5 = 18

5/2 + 18

18 can be writen as a fraction which is 36/2

5/2 + 36/2 = 41/2

in conclusion the simplified form of the expression is 41/2

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find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points. f(x, y)

Answers

The local maxima is(1,0) , local minima is indefinite and the saddle point is (1,0).

As per given in the question ,

f(x,y)=[x2+1 ]

[-2y ]

The critical points are therefore (1,0) and (1,0).

The Hessian is currently

∇²f(x,y)=[−2x 0

0 −2]

2 and 2 are the eigenvalues of the function 2f(1,0).

As a result, (1,0) is a saddle point and 2f(1,0) is indefinite.

Two and two are the eigenvalues of 2f(1,0).

As a result, (1,0) is a maximum and 2f(1,0) is negative definite.

Critical point: If f (p) = 0, then a point p U is f's critical point.

In light of this, the tangent plane to z = f when f is differentiable (x) at (p, f (p)) is horizontal.

Theorem: Assume that f exists and possesses a local extremum at position p. Then, p is a f critical point, with the result that f (p) = 0.

Example: Take into account f (x, y) = x 2 y 2. Once again demonstrating that (0, 0) is the only crucial point of f, fx = 2x = 0 and fy = 2y = 0

However, (0, 0) is not a f local maxima.

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A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?

Answers

255 biology and 192 sociology textbooks were sold in a week.

What is linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.

Step 1:

Let x be the number of biology textbooks and y be number of sociology textbooks.

x + y = 447 ------(1)

x - y = 63 ------(2)

Step 2:

Adding (1) and (2), we get

2x = 510

x = 255

Step 3:

Subtracting (1) from (2), we get

2y = 384

y = 192

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use distributive property to create an equivalent expression to 40+4x.

Answers

Answer:

4(10+x)

Step-by-step explanation:

find the gcf: 4

divide everything by the gcf: 4(10+x)

Answer:There are 3 answers 4(10+x), 4(10)+4(x), 40+4x

PLEASE HELP ITS GEOMETRY ASAP HELP ME

Answers

M(-2,1)
L(-7,4)
K(-4,8)
Next coordinates after translation 8 units to the left

M(6,1)
L(1,4)
K(4,8)
Next coordinates after reflection across x

M(6,-1)
L(1,-4)
K(4,-8)
The final answers are the ones above. (6,-1), (1,-4), (4,-8)

Hello please solve this with steps
List the possible rational zeros of
f(x)= x^3-6x^2+6x-18 using the rational zero theorem

Answers

Answer:

±{1, 2, 3, 6, 9, 18}

Step-by-step explanation:

You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.

Rational root theorem

The rational root theorem tells you the possible rational zeros are of the form ...

±{divisors of the constant term} / {divisors of the leading coefficient}

Here, the leading coefficient is 1, so its only divisor is 1.

The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.

The possible rational roots are ±{1, 2, 3, 6, 9, 18}.

Additional comment

A graph shows the only real root is between 5 and 6, so none of the roots are rational.

A sales tax is charged on some items at a grocery store but not charged on others. When the
taxable items total t dollars and the non-taxable items total n dollars, the total bill is 1.06t +
n dollars. Malia went shopping yesterday. She spent $20 on taxable items and $8.20 on non-
taxable items.
How much was Malia's total grocery bill?

Answers

Answer:24.90

Step-by-step explanation: My brain

Here are the shopping times (in minutes) of nine shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 6 .)

Answers

The answer for all 3 of the boxes is 3. The number of observations for each class interval of a variable is shown in group frequency distributions.

Complete the grouped frequency distribution for the data ?

DISTRIBUTION OF GROUPED FREQUENCIES

The greatest score is H, while the lowest is L.

By dividing the range by a number of groupings or classes, you can estimate the class width w.

Establish the class intervals.

Add up the scores for each period in the appropriate number.

The shopping time (in minutes) of the nine shoppers are:

15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged everything from least to greatest.)

We can see, that 3 shoppers shopped for 15-20 minutes.

And, 3 shoppers shopped for 21-26 minutes.

And finally, 3 shoppers shopped for 27-32 minutes.

So the answer for all 3 of the boxes is 3.

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ashley was born on 06/10/1961. how many 8 digit codes could she make using the digits in her birthday

Answers

3360, 8 digit codes could she make using the digits in her birthday.

What is the 4 digit code?

A quick, thorough, and evidence-based method for diagnosing the full range of outcomes seen in people who have had prenatal alcohol exposure is the 4-Digit Code.

Given the date:

Birth date = 12/24/2002 06/10/1961

Number of digits = 8 = 8! = (8*7*6*5*4*3*2*1) = 40320

Repeated digits :

digit 6 = 2 times = 2! = 2*1 = 2

digit 1 = 3 times = 3! = 3*2*1 = 6

Therefore the number of 8 digit codes that can be formed is :

8! / (2! * 3!)

40320 / (2 * 6)

40320 / 12

= 3360

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help help help help help help help help help help help help help help help help help help help help help hel

1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x

A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare
2. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)

A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare
3. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16

4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x

Answers

1. Which equation represents a line that has a slope of 2 and passes through the origin?

A y=2x

B. y=x+2

C. y x

D. y=-x

2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?

A. F = 12(7)

B. F=12(7)+1.50

C.=12(150)+7

D.=12+2(1.50)

3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?

A. P15

B. P13.50

C. P14.50

D. P16

4.Which equation represents a vertical line?

A. y =2x

B. x = 2

C. y = 3

D. y = -x

dory orders three soft tacos and three double Deckers for 11.25. Nemo pays 10.00 for four soft tacos and two double Deckers. write a system of equations that represent the lunch orders for dory and Nemo. Use x to represent soft tacos and y to represent double Deckers.

Answers

Answer:

Soft tacos are $1.25 each, while double deckers are $2.5 each.

(I didn't have time for a step by step explanation at the moment)

Sorry

need help on this one

Answers

Answer:

19 units

Step-by-step explanation:

You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.

Midline

The midline of a triangle is half the length of the parallel base:

LM = 1/2(IJ)

6x +1 = 1/2(-6x +56) . . . . . substitute expressions

6x +1 = -3x +28 . . . . . . . simplify

9x = 27 . . . . . . . . . . . . sdd 3x-1

x = 3

Now, we can find LM:

6x +1 = 6(3) +1 = 19

The measure of LM is 19 units.

Simplify
f(x) = 8x+5 find f(5)

Answers

Answer: To find the value of f(5), we need to substitute 5 for x in the expression f(x) = 8x+5. This gives us:

f(5) = 8*5+5 = 45

So, the value of f(5) is 45.

Solve your system of equations from part A using elimination. Then, complete the statement. Type the correct answer in each box. Use numerals instead of words. The test has questions worth 2 points and questions worth 4 points

Answers

There are 15 two-point questions and 5 four-point questions.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Let x be two-point questions and y be four-point questions. We know that there are 20 questions so the number of two-point questions plus the number of four-point questions equals 20. So x + y = 20. We also know that the total number of points is 50, so 2x + 4y = 50.

Solving the system:

1) x + y = 20

2) 2x + 4y = 50

Isolate x in 1) to get x = 20-y, then plug into 2)

2(20-y) + 4y = 50

2y=10

y = 5,

It means that there are 5 four-point questions. Plug y = 5 into either equation to get x = 15 so there are 15 two-point questions.

x + y = 20

x + 5 = 20

x = 15

Hence, there are 15 two-point questions and 5 four-point questions.

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Answer:

Step-by-step explanation:

the test ha 65 questions worth points and 5 questions worth 4 points

What is the approximate percentage of women with platelet counts between 3 and 4.1?

Answers

The approximate percentage of women with platelet count between 3 and 4.1 is 350

How to solve for approximate percentage?

We should know that platelet deals the cells that are found in our body which assemble together when they discover bad blood in the cells.

The range of women is given as 3-4.1

The average of the women is [tex]\frac{3+4.1}{2}=\frac{7.1}{2}[/tex]

Simplifying the expression we have

= 3.5

The appromimate percentage is 3.1*100=350 women

In conclusion the approximate percentage of women with blood platelet is 350 women

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36. Rapid City is having its annual citywide celebration. The city wants to rent a bumper-car ride. The pieces used to make the floor are 4 foot-by-5 foot rectangles. The ride covers a rectangular space that is 40 feet by 120 feet. a. How many rectangular floor pieces are needed? b. The ride costs $20 per floor piece and $10 per bumper car. How much would it cost Rapid City to rent the floor and the bumper cars? (You will need to decide how many bumper cars will be appropriate.)

Answers

Answer:

a. 240pieces

b. 4800+ 10x

Step-by-step explanation:

a. 40÷4=10, 120÷5=24, 10×24=240

b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars

y=3x + 1 if x =-2 then y=?

Answers

Answer:

Step-by-step explanation:

If x equals -2 then you multiply 3 times -2 which equals -6 then add 1. Your total then is -5. Y equals -5

yeah if x equals -2 then u have to multiply 3 times -2 and that equals -6. then u have to add 1. so therefore y equals -5

This morning, Russell took a history test. He got 25 out of 50 problems right. What percentage did Russell get right?

Answers

Answer: 40%

Step-by-step explanation:

What is 2 1/4 divided by 4????
1. 5/8
2. 1/10
3. 10
4. 1 3/5

Answers

Step-by-step explanation:

2 1/4 = 9/4

9/4 ÷ 4

9/4 x 1/4

9/16

so neither of these answers?

What is the slope of the line that passes through the points (-8, -1) and
(-8, -11)? Write your answer in simplest form.

Answers

Answer:

Step-by-step explanation:

The slope of a line is defined as the change in y-coordinate divided by the change in x-coordinate between two points on the line. In this case, the change in y-coordinate between the two points is -11 - (-1) = -10, and the change in x-coordinate is 0 since both points have the same x-coordinate. Therefore, the slope of the line that passes through the points (-8, -1) and (-8, -11) is -10/0, which is undefined.

solve
2(2.1z+4.5)<21.6

Answers

The solution to the given inequality 2(2.1z + 4.5) < 21.6 to solve for the unknown value of z is z < 3

How to solve inequality?

Inequality refers to a statement that is of two quantities in which one is specifically less than (or greater than) another.

The symbols of inequality includes;

Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤

2(2.1z + 4.5) < 21.6

open parenthesis

4.2z + 9 < 21.6

substract 9 from both sides

4.2z < 21.6 - 9

4.2z < 12.6

divide both sides by 4.2

z < 12.6 / 4.2

z < 3

Hence, z < 3 satisfies the value of z in the inequality 2(2.1z + 4.5) < 21.6