Mathematics, 16.08.2020 01:01 Kuwillalean38

Which of the following pairs of functions are inverses of each
other?

Answers: 1

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Answers

Answer from: marpinator

Step-by-step explanation:

For this problem, let's find the inverse for all f(x) and see which pairs with the g(x). To find the inverse, you replace the x with y and y with x. Then you solve for y.

A. Incorrect

$y=\frac{x-8}{4} +9$ [replace x with y and y with x]

$x=\frac{y-8}{4} +9$ [subtract both sides by 9]

$x-9=\frac{y-8}{4}$ [multiply both sides by 4]

4(x-9)=y-8 [add both sides by 8]

4(x-9)+8=y

This does not match g(x), therefore, they are not inverses of each other.

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B. Incorrect

y=4(x-12)+2 [replace x with y and y with x]

x=4(y-12)+2 [subtract both sides by 2]

x-2=4(y-12) [divide both sides by 4]

$\frac{x-2}{4} =y-12$ [add both sides by 12]

$\frac{x-2}{4} +12=y$

This does not match g(x), therefore, they are not inverses of each other.

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C. Correct

$y=3(\frac{x}{2})-4$ [replace x with y and y with x]

$x=3(\frac{y}{2} )-4$ [add both sides by 4]

$x+4=3(\frac{y}{2} )$ [divide both sides by 3]

$\frac{x+4}{3} =\frac{y}{2}$ [multiply both sides by 2]

$\frac{2(x+4)}{3} =y$

This matches g(x), therefore, they are inverses of each other.

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D. Incorrect

$y=3(\frac{2}{x} )-10$ [replace x with y and y with x]

$x=3(\frac{2}{y} )-10$ [add both sides by 10]

$x+10=3(\frac{2}{y} )$ [divide both sides by 3]

$\frac{x+10}{3} =\frac{2}{y}$ [multiply both sides by y]

$(y)(\frac{x+10}{3} )=2$ [multiply both sides by $\frac{3}{x+10}$ or divide by $\frac{x+10}{3}$ ]

$y=\frac{6}{x+10}$

This does not match g(x), therefore, they are not inverses of each other.

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After going through each problem, we found that the correct answer is C.

Answer from: Quest

this was already solved by me with a different person. if you look it up in the search bar at the top of the page, you will get the answer.

step-by-step explanation:

Answer from: Quest

it is b)

hope this : )

step-by-step explanation:

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