Question

Given the function f(x) = 2^x, find the value of f^−1(32).

a. f^−1(32) = 0
b. f^−1(32) = 1
c. f^−1(32) = 5
d. f^−1(32) = 16

Answer 1

`f(x)= 2^(x)`

We are to find the value of
`f^(-1)(32)`

First we need to find the inverse of f(x) . The inverse of
`2^(x)` is
`(ln(x))/(ln(2))`.

Steps to find inverse of f(x) are shown below in the image.

So
`f^(-1)(32)` =
`(ln(32))/(ln(2))=5`

Therefore, the correct answer is option C