Answer
f(g(x))= x
g(f(x))= x
Work Step by Step
The question asks to prove that f and g are inverses of each other.
So, to be able to solve for f(x), first, you replace the (x) by g(x). G(x) is $\frac{1}{x}$, so you replace g(x) by $\frac{1}{x}$. Then you solve for f(x).
Meaning that the x in the f(x) equation is going to be replaced by $\frac{1}{x}$. Then you solve.
1 over $\frac{1}{x}$ equals to $\frac{1}{1}$$\times$$\frac{x}{1}$. It equals to $\frac{x}{1}$, which can be simplified to x.
Same process for g(x).
These equations say that the cube function and the cube root function, when composed, cancel each other.