How do I evaluate composite functions?

Suppose you have 2 functions: f(x) = 3x², g(x) = log₃(x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log₃(x) ( = g(x) ), then f(g(x)) = f(y) = 3y² = 3[log₃(x)]².

The part that people tend to find difficult is remembering what it means to apply a function. A simple subsitution makes this much easier. Whilst the above situation makes it seem easy, consider how much more confusing it could be if f(x) = [x⁷ + 9x⁵ + e^5x + cos(x^-1/3)]/[sin(e^x/6) + 1729*x], and g(x) was something similarly complicated; a simple substitution can do wonders and will help prevent confusion.