Answers
Answer: They are inverses of each other
============================================================
Explanation:
We need to check two things:
f(g(x)) = xg(f(x)) = xIf both of those equations are true, then f and g are inverses of each other.
----------------
Part 1
[tex]f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x\\\\[/tex]
So far, so good. Now we need to check the other equation mentioned.
------------------
Part 2
[tex]g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\[/tex]
That works out as well. Both equations mentioned are true, which confirms the two original functions are inverses of one another.
Related Questions
Miss Johnson has in her classroom closet 32 boxes with 245 counters. She wo
to redistribute them and share them equally in 25 bags for a class activity.
a) How many counters will she put in each bag?
b) Will she have any counters left? If yes, how many?
Answers
Answer:
she will put 9 counters in each bag
she will have 20 counters left over
Answer:
a. 9 each
b. yes she will have 20 left
Step-by-step explanation
245/25=9.8 but if equally it will be 9 with a remainder of 20
that solves everything
I need some help please
Answers
The answer is A.
A negative x a negative equals a positive so the square root of a negative value cannot be a negative value.
You are delt 1 card from a 52 card deck. Find the probability that you are not dealt a 10
Answers
Answer:
Step-by-step explanation:
There are 4 tens.
There are 48 cards that are not a 10. The probability of drawing 1 of the 48 is
P(~10) = 48/52 which is quite high as you might imagine.
please help me on this, thank you
Answers
45 - 4 =41 and x is 20.5 or 20 1/2
2a+b+c=9 a+2b+c=8 a+b+2c=11
Answers
[tex] \: \: \: \: \: \: [/tex]
# 2a+b+c=9answer
[tex]a = \frac{9}{2} - \frac{1}{2} b - \frac{1}{2} c[/tex]
#a+2b+c=8answer
[tex]a = 8 - 2b - c[/tex]
#a+b+2c=11answer
[tex]a = 11 - b - 2c[/tex]
refer to the attachment for explanationhope it helpscan someone plssssssss help me
Answers
Answer:quizlet helps
Step-by-step explanation:
Identify the range of values for x.
Answers
Answer: Overall, the steps for algebraically finding the range of a function are:
Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x). ...
If you can't seem to solve for x, then try graphing the function to find the range.
Step-by-step explanation:
find the solution to the following system using substitution. y = - 4 + 9 y = 3x - 5
Answers
Answer:
1/2, 11/6
Step-by-step explanation:
y=-4+9y
9y-y=4
8y=4
y=1/2
3x-5=1/2
3x=5+1/2=11/2
x=11/6
f(x)=x+1/x-2
find the inverse
Answers
Could be your answer
You are designing a new, larger coral reef habitat that will stun visitors with its size and vibrant colors. The tank requires special glass to protect this delicate environment. The glass costs $25,000 + a 10% engineering fee + a 5% shipping fee. The shipping fee is calculated on the cost of the glass plus engineering charges. What is the total cost of the glass, including fees?
Answers
Answer:
$28,875
Step-by-step explanation:
First, we would have to find 10% of $25,000
10% of $25,000 = $2,500
Now, we have to add the 2 values together
$25,000 + $2,500 = $27,500
Now, we can find the shipping fee, since it includes the engineering fee
5% of $27,500 = $1,375
Now, we can add the shipping fee to find the total
$27,500 + $1,375 = $28,875
A study of more than 3,000 toco toucans found that their weights were approximately Normally distributed, with a mean
of 20 ounces and a standard deviation of 2.3 ounces. Let Y be the weight of a randomly chosen toco toucan. Which of
the following correctly interprets the value of P(Y < 16)?
Find the Z-table here.
O P(Y< 16) = 0.50. About 50% of all toco toucans weigh less than 16 ounces.
OP(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ounces.
O P(Y < 16) = 0.959. About 95.9% of all toco toucans weigh less than 16 ounces.
P(Y < 16) = 0.041. About 4.1% of the toco toucans from this group weigh less than 16 ounces.
O P(Y< 16) = 0.959. About 95.9% of the toco toucans from this group weigh less than 16 ounces.
Answers
Using the normal distribution, it is found that the correct option is:
P(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ouncesIn a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 20 ounces, hence [tex]\mu = 20[/tex].Standard deviation of 2.3 ounces, hence [tex]\sigma = 2.3[/tex]P(Y < 16) is the p-value of Z when X = 16, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 20}{2.3}[/tex]
[tex]Z = -1.74[/tex]
[tex]Z = -1.74[/tex] has a p-value of 0.041.
This is valid for the entire population, hence, the correct interpretation is:
P(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ouncesA similar problem is given at https://brainly.com/question/24663213
What is the value of the expression 2/5m−1/3 when m = 3?
1/15
13/15
23/15
I don't know.
Answers
Answer:
13/15
Step-by-step explanation:
i took the test :)
What is the value of x and y?
Answers
Answer:
x = 90y = 43Step-by-step explanation:
The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.
x° = 90°
__
The acute angles in a right triangle are complementary.
y° = 90° -47°
y° = 43°
The polygons are similar. Find the value of each variable.
Answers
[tex]\\ \sf{:}\dashrightarrow \dfrac{4}{x}=\dfrac{6}{9}[/tex]
[tex]\\ \sf{:}\dashrightarrow 6x=36[/tex]
[tex]\\ \sf{:}\dashrightarrow x=6[/tex]
#y
[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{12}{18}[/tex]
[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{2}{3}[/tex]
[tex]\\ \sf{:}\dashrightarrow 3y=24[/tex]
[tex]\\ \sf{:}\dashrightarrow y=8[/tex]
Here we go
4/x=6/94/x=2/32/x=1/3x=6And
y/12=12/1818y=12²18y=144y=8House of Mohammed sells packaged lunches, where their finance department has established a
weekly relationship between its Revenue R, in dollars and the number of lunches x, as R=x(82−x)
(a) Write the revenue R, in the form R=ax2+bx+c (b) What is the revenue when 35 lunches are sold? (c) Explain why the graph of R has a maximum.
(d) Write R in the form a(x−h)2+k
(e) How many lunches must be sold for them to achieve their maximum revenue?
(f) State the company's maximum revenue.
(2 marks) (2 marks) (2 marks)
(5 marks)
(2 marks) (2 marks)
(g) Complete the following table of values and graph the Revenue equation using the ordered pairs
(x , R). Label the coordinates of the vertex.
x
10
20
30
40
50
60
70
80
90
R
( 10 marks)
Answers
The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d) R = -1·(x - 41)² + 1,681(e) 41(f) $1,681Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
R = -x² + 82·xWhere, the constant term, c = 0
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
The revenue when 35 lunches are sold, R = $1,645
(c) The given function for R is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function R is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]
Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]
The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
The maximum revenue of the company is $1,681Learn more about the quadratic function here:
https://brainly.com/question/2814100
( 4 1 + 4 5 ) ^ 2 + 4 3 =
Answers
(41 + 45) ^ 2 + 43
(86) ^ 2 + 43
7396 + 43
7439
Answer: 7,439
Step-by-step explanation:
(86)^2 + 43
7396 + 43 = 7,439
I'm pretty sure that the other user has the same answer. (godlike74)
Please help with this question
Answers
Answer:
D
Step-by-step explanation:
The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.
-hope it helps
Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.
Step-by-step explanation:
You wish to buy a new skateboard. To earn money, you sell your baseball cards to
your friends for $2.50 each. If the new skateboard costs $98, what is the minimum number
of baseball cards you will have to sell?
Answers
The minimum cards u need to sell is
98/2.50 which is 39.2 but you can’t sell cards in fraction so the final answer is 40
Consider the functions f(x) = 10^x and g(x)= f(x+4)
How will the graph of the function g differ from the graph of f ?
A) the graph of the function g is the graph of function f shifted 4 units down
B) the graph of the function g is the graph of function f shifted 4 units to the right
C) the graph of the function g is the graph of function f shifted 4 units to the left
D) the graph of the function g is the graph of function f shifted 4 units up
Answers
Help ASAP please. I really need the answer as soon as possible
Answers
Answer:
y intercept is 6 and the rate of change is Y=3x+6
Step-by-step explanation:
Answer:
y intercept = 6
rate of change = -4
Step-by-step explanation:
the line hits the y axis at 6 so that is the y intercept
The line falls 4 and goes over 1
I hope this helps!!
A mechanic is paid $61,490 in salary for a year. Assuming there are 26 pays in a year, what is her biweekly (average) salary? $30,745 $3,074.50 $1,182.50 $2,365
Answers
Answer:
$2,365
Step-by-step explanation:
Divide $61,490 by 26...
Explain in your own words the steps to dividing decimals by decimals.
Answers
2: If the divisor is not a whole number, then move the decimal place
places to the right to make it a whole number. Then move the decimal place in the dividend the same number of places to the right (adding some extra zeros if necessary.)
3: Divide as usual. If the divisor doesn't go in evenly, add zeros to the right of the dividend and keep dividing until you get a 0
0
remainder, or until a repeating pattern shows up.
4: Put the decimal point in the quotient directly above where the decimal point now is in the dividend.
5: Check your answer against your estimate to see if it's reasonable.
Using powers of 10, which would be the best choice for the first number to subtract in the division problem 14,941 ÷ 98?
Answers
Answer:
0.152
Step-by-step explanation:
Can I get the answers for all the questions and if you can explain how you got it that would help PLSSSSS!!!!
Answers
Estimate 196.999 ÷ 1.582?
Answers
Answer:
124.5252844501
Step-by-step explanation:
to estimate we have 125
Astudent built a scale model of his house using a scale in which 3 inches represents 15 feet.The height of his real house is 45 feet.What is the height of the scale model in inches?
NEED HELP ASAP
Answers
Answer:
9 inches
Step-by-step explanation:
4x+4 =
What is the answer to this please help
Answers
Answer:4(x+1)
Step-by-step explanation:
4x+1
I need help with this.
Answers
Answer:
check online for more information
Consider continuous functions f, g, h, and k. Then complete the statements.
The function that has the least minimum value is function (options) F, H, G, K
The function that has the greatest minimum value is function (options) F, H, G, K
.
Answers
It wouldn't let me post the answer. See images for the answer and explanation
The function that has the least minimum value is function F & the function that has the greatest minimum value is function K.
What are the minimum values of the functions?Given:
Consider continuous functions f, g, h, and k.A graph is given in the attached image.Find:
The function that has the least minimum value is function.the function that has the greatest minimum value is function.Solution:
From the question, we get;
[tex]h(x) = 2(x-1)^{2}[/tex]
⇒ h(x)min = 0
⇒ g(x)min = -5
⇒ f(x)min = -7
⇒ k(x)min = 7
So, f(x)min < g(x)min < h(x)min < k(x)min
Therefore, The function that has the least minimum value is function F & the function that has the greatest minimum value is function K.
To learn more about the minimum of functions, refer to:
https://brainly.com/question/9180672
#SPJ2
What is the solution to this problem
Answers
(49-46) + ( 4 x 3 )
(3) + (12)
= 15