Function composition is denoted by

, or f o g in plain text. Some sources may skip the circle, but I would expect them to note this convention explicitly. In any case, it is much better to write a bit more explanations than to let people wonder about notation.

You showed that

, which means that g is the (right) inverse of f. This is the relationship between the functions. There are many other relationships, e.g.,

,

,

,

,

, etc., but apparently they are not relevant to the question (except maybe the first).

Note also that both sides of equality should have the same type: either functions or real numbers. For example,

is a function (the composition of f and g), while x is a number. So, writing

is not the best. One should write

or

where

is the identity function.

Since

, you can cancel 1994 applications

in

and get

. In evaluating this, note also that

(this can be verified directly; it also follows from

and

).