let f(x) = x^3 − 2 and g(x) = ^3√ x − 2

Question

I can't figure out if these are inverses for each other, I don't know how to put in f(g(x)) or g(f(x)) and have an answer

Answer 1

If y = x^3-2
y+2 = x^3
x = ∛(y+2)

That means that

∛(x+2) is the inverse of x^3-2

To check, you know that f(f^-1(x)) = x and f^-1(f(x)) = x

So, if g(x) = f^-1(x),
f(g) = g^3-2
= (∛(x+2))^3 - 2
= x+2-2
= x

and the same for g(f).