contestada

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

Respuesta :

[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
Ver imagen 11beehshahbaz

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