Use the following table to evaluate (f^-1 of g)(3)

x 1 2 3 4 5
f(x) 3 4 1 5 2
g(x)2 3 4 5 1

How do inverses of f work in problems like this?

You could add a row with values for f^-1 if you wish:

f(1) = 3 ⇒ f^-1(3) = 1
f(2) = 4 ⇒ f^-1(4) = 2
f(3) = 1 ⇒ f^-1(1) = 3
f(4) = 5 ⇒ f^-1(5) = 4
f(5) = 2 ⇒ f^-1(2) = 5

Then

g(3) = 4
(f^-1 of g)(3) = f^-1(g(3)) = f^-1(4) = 2.

Of course, you wouldn't need to do all the calculations I did above; you would only need the x-value for which f(x) = 4, which is 2.