Suppose f (x) = x^3 + x

and g(x) = f^-1(x). Find g'(2).

I am confused about how to find the inverse of f because I can't isolate y. Could you please help? Thanks!

x=y^3+y

well, you can use the method of
http://www.ms.uky.edu/~corso/teaching/math330/Cardano.pdf