Question

Which of the following pairs of functions are inverse’s of each other?

Answer 1

The answers in C are inverses of each other.

In order to find the inverse of any equation, you simply switch the x and f(x) values and then solve for the new f(x). What it will result in is your new inverse function. If we do this for each of the problems above, only one will produce the second equation properly. See the work below for how to do it for C.

f(x) = 11x - 4 ---> Switch the x and f(x)

x = 11f(x) - 4 ----> Add 4 to both sides

x + 4 = 11f(x) ----> Divide both side by 11

$\frac{x+4}{11}$ = f(x) ----> Now put in the correct order

f(x) = $\frac{x+4}{11}$

Since our inverse matches the g(x) function, this means that C is the correct answer.