Function operations and composition of functions worksheet answers

In the composition of (f o g) (x) the domain of function f becomes g(x). The domain is a set of all values which go into the function. Example: If f(x) = 3x+1 and g(x) = x² , then f of g of x, f(g(x)) = f(x²) = 3x²+1. If we reverse the function operation, such as f of f of x, g(f(x)) = g(3x+1) = (3x+1)².

That's pretty much all there is to "operations on functions" until you get to function composition. Don't let the notation for this topic worry you; it means nothing more than exactly what it says: add, subtract, multiply, or divide; then simplify and evaluate as necessary.

The composition of two functions f and g is the new function h, where h(x) = f(g(x)), for all x in the domain of g such that g(x) is in the domain of f. The notation for function composition is h = f • g or h(x) = (f • g)(x) and is read as 'f of g of x'.