Question

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

Answer 1

Answer:

D.

Step-by-step explanation:

f(x) is multiplication

g(x) is division

Therefore these are opposite functions

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Answer 2

Answer:

A. $f(x)=\frac{12}{x}-18$ and $g(x) = \frac{12}{x+18}$

Step-by-step explanation:

For find the inverse of a funtion we have to solve for x in the equation:

$f(x)=\frac{12}{x}-18$

First, replace f(x) to y and solve for x as:

$y=\frac{12}{x}-18$

$y+18=\frac{12}{x}$

$x(y+18)= 12$

$x = \frac{12}{y+18}$

and finally we interchange y and x as:

$y = \frac{12}{x+18}$

and replace y by g(x):

$g(x) = \frac{12}{x+18}$

So, the inverse of the function $f(x)=\frac{12}{x}-18$ is $g(x) = \frac{12}{x+18}$