Answer:
The only pair of functions that are inverses of each other are the ones for option D.
Step-by-step explanation:
Two functions, f(x) and g(x), are inverses if and only if:
f( g(x) ) = x
g( f(x) ) = x
So we need to check that with all the given options.
A)

then:

This is clearly different than x, so f(x) and g(x) are not inverses.
B)
![f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B11%2Ax%7D%20%5C%5Cg%28x%29%20%3D%20%28%5Cfrac%7Bx%7D%7B11%7D%20%29%5E3)
Then:
![f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Csqrt%5B3%5D%7B11%2A%28%5Cfrac%7Bx%7D%7B11%7D%29%5E3%20%7D%20%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%5E3%7D%7B11%5E2%7D%20%7D%20%3D%20%5Cfrac%7Bx%7D%7B11%5E%7B2%2F3%7D%7D)
This is different than x, so f(x) and g(x) are not inverses.
C)

Then:

Obviously, this is different than x, so f(x) and g(x) are not inverses.
D)

Then:

In this case we can conclude that f(x) and g(x) are inverses of each other.