Question

F(x) = 9x + 1, find f–1 (f (3)).

Answer 1

For this case we have the following function:

`image`

Rewriting we have:

`image`

To find the inverse function, we must clear the value of x.

We have then:

`image`

`x=(y-1)/(9)`

Returning the change of variables we have:

`f(x)^(-1)=(x-1)/(9)`

The original function evaluated at x = 3 is:

`image`

We evaluate the inverse function for x = f (3) we have:

`f(28)^(-1)=(28-1)/(9)`

`f(28)^(-1)=(27)/(9)`

`f(28)^(-1)=3`

Answer:

The value of the function is:

`f(28)^(-1)=3`