Question

f(x) = 9x + 1, find f–1 (f (3)).

Answer 1

For this case we have the following function:

$f (x) = 9x + 1$

Rewriting we have:

$y = 9x + 1$

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

We have then:

$9x = y-1$

$x=\frac{y-1}{9}$

Returning the change of variables we have:

$f(x)^{-1}=\frac{x-1}{9}$

The original function evaluated at x = 3 is:

$f (3) = 9 (3) + 1 f (3) = 27 + 1 f (3) = 28$

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

$f(28)^{-1}=\frac{28-1}{9}$

$f(28)^{-1}=\frac{27}{9}$

$f(28)^{-1}=3$

Answer:

The value of the function is:

$f(28)^{-1}=3$