The best way to work with functions is through Algebrator, in which many "wizards" simplify operations such as compositions.  To cite a random example, however, I can choose the following functions:

f(x)=2x+3

g(x)=3x^2-3x+4

The composition of these functions become either f(g(x)) or g(f(x)).  To solve for f(g(x)), every instance of 'x' in 2x+3 is replaced by the expression for g(x).  Conversely, every instance of 'x' in g(x) is replaced by the expression for f(x). 

The following images show the usage through Algebrator as well as two approaches for a manual solution through doyourmath.com.