If f(x) and g(x) are two functions such that f(g(x)) = x then f(x) and g(x) are

They are inverse functions though to be completely thorough your teacher should have also put g(f(x)) = x as well. Though I can see what your teacher is aiming for at least.

The idea is that whatever the output of g(x) is, it's plugged into f(x) and the initial input is the result. So g(x) takes a step forward and f(x) takes a step back undoing everything g(x) did. Which is exactly what an inverse operation does.