Verified Answer :

mun52022

The first answer choice is your answer :)

isyllus

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

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