Question

Please help: What is the inverse of the function below?

Answer 1

The answer is D

Explanation:

In order to find out the inverse of the function, you have to express a new function where the independent variable must be "y" instead of "x".

So, you have to reorganize the base function and then free the variable "x".

`f(x)=2^x+6\\f(x)=y\\y=2^x+6\\2^x=y-6\\log_2(2^x)=log_2(y-6)\\x*log_2(2)=log_2(y-6)\\log_2(2)=1\\x=log_2(y-6)\\`

Then, we recall "y" as "x" and
`x=f^-^1(x)`

Finally, the answer is:

`f^-^1(x)=log_2(x-6)`

Answer 2

D.
`f^(-1)(x)=\log_2{(x-6)}`

Explanation:

Solve x = f(y) for y:

x = 2^y +6

x -6 = 2^y . . . . subtract 6

log2(x -6) = y . . . . take the log base 2 . . . . matches choice D