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 ).