You should KNOW 

1. That functions can be added, subtracted, multiplied and divided and how these operations on functions are defined. 

2. That two or more functions can be composed to produce another function, by applying the original functions one at a time, and that if f and g are two function, their composition is denoted by f o g where  (f o g)(x) = f(g(x)).

3. That the order of the composition matters, so that f o g is not 
necessarily the same as g o f. 

4. That more involved functions can often be viewed as composition of simpler functions. 
     

You should be ABLE TO

1. Calculate f+g, f-g, f.g, f/g for functions f, g given by formulas.

2. Calculate the composition of two or more given functions and describe the domains and ranges of these compositions.

3. Decompose a function into a composition of simpler functions, recognizing that this might be done in more than one way.