Question

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

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 $\frac{ln(x)}{ln(2)}$.

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

So $f^{-1}(32)$ = $\frac{ln(32)}{ln(2)}=5$

Therefore, the correct answer is option C