For this case we have the following function:
[tex] f (x) = 9x + 1
[/tex]
Rewriting we have:
[tex] y = 9x + 1
[/tex]
To find the inverse function, we must clear the value of x.
We have then:
[tex] 9x = y-1
[/tex]
[tex] x=\frac{y-1}{9} [/tex]
Returning the change of variables we have:
[tex] f(x)^{-1}=\frac{x-1}{9} [/tex]
The original function evaluated at x = 3 is:
[tex] f (3) = 9 (3) + 1
f (3) = 27 + 1
f (3) = 28
[/tex]
We evaluate the inverse function for x = f (3) we have:
[tex] f(28)^{-1}=\frac{28-1}{9} [/tex]
[tex] f(28)^{-1}=\frac{27}{9} [/tex]
[tex] f(28)^{-1}=3 [/tex]
Answer:
The value of the function is:
[tex] f(28)^{-1}=3 [/tex]
