Question

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

f−1(3) = 2
f−1(3) = 3
f−1(3) = 9
f−1(3) = 18

Answer 1

The first answer choice is your answer :)

Answer 2

`f^(-1)(3)=2` is correct

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