[tex]f(x)= 2^{x} [/tex]
We are to find the value of [tex] f^{-1}(32) [/tex]
First we need to find the inverse of f(x) . The inverse of [tex] 2^{x} [/tex] is [tex] \frac{ln(x)}{ln(2)} [/tex].
Steps to find inverse of f(x) are shown below in the image.
So [tex] f^{-1}(32) [/tex] = [tex] \frac{ln(32)}{ln(2)}=5 [/tex]
Therefore, the correct answer is option C
