Composite functions are formed when multiple functions are combined together. It is a function of a function.

For example, the functions \(f(x)\) and \(g(x)\) can be combined together to form a composite function.

• Putting \(g(x)\) into \(f(x)\), i.e. \(f(g(x))\) forms the composite function \(fg(x)\).
• Putting \(f(x)\) into \(g(x)\), i.e. \(g(f(x))\) forms the composite function \(gf(x)\).

Tip: \(fg(x)\) is not necessarily the same composite function as \(gf(x)\). The order of the functions matter.

The notation is different when both functions are the same:

\(f(f(x)) = f^2(x)\)