studying for clep calculus exam inverse functions and derivates

I was taking a practice clep calculus exam I found online and I do not understand how the correct answer was derived.

f(x) = x^3 + x. and h(x) is an inverse function of. find h'(2)??? I know that f(h(x)) = x and if f'(h(x))h'(x) = 1
h'(x) = 1/f'(h(x)). My understanding is that if f(2) = 10 then h(10) = 2 because they are inverses. Could somebody help me with my misunderstanding? I think the correct answer was 1/4.