Answer:
[tex]f^{-1}(3)=2[/tex] is correct
Step-by-step explanation:
Given the function [tex]f(x) = \log_2(x + 6)[/tex]
We need to find [tex]f^{-1}(3)[/tex]
First we find the inverse of the function
[tex]y= \log_2(x + 6)[/tex]
Switch x and y
[tex]x= \log_2(y + 6)[/tex]
Solve for y
[tex]2^x=y + 6[/tex]
[tex]y=2^x-6[/tex]
[tex]\therefore, f^{-1}(x)=2^x-6[/tex]
Put x=3
[tex]f^{-1}(3)=2^3-6\Rightarrow 8-6=2[/tex]
Thus, [tex]f^{-1}(3)=2[/tex] is correct
