Question

Given the function f(x) = log2(x + 6), find the value of f−1(3).

Answer 1

Answer:

$f^{-1}(3)=2$ is correct

Step-by-step explanation:

Given the function $f(x) = \log_2(x + 6)$

We need to find $f^{-1}(3)$

First we find the inverse of the function

$y= \log_2(x + 6)$

Switch x and y

$x= \log_2(y + 6)$

Solve for y

$2^x=y + 6$

$y=2^x-6$

$\therefore, f^{-1}(x)=2^x-6$

Put x=3

$f^{-1}(3)=2^3-6\Rightarrow 8-6=2$

Thus, $f^{-1}(3)=2$ is correct

Answer 2

The first answer choice is your answer :)