Composition

Objective

Evaluate and simplify composite functions f(g(x)).

What it means

Composition combines two functions so the output of one becomes the input of the other. (f ∘ g)(x) = f(g(x)) means you evaluate g first, then plug that result into f.

Key terms

Composite function

f(g(x)), read 'f of g of x'

Inner function

The function evaluated first, g(x)

Outer function

The function applied second, f(...)

Rules to remember

• Always evaluate the inner function first.
• Substitute the entire inner result into every x of the outer function.
• f(g(x)) is generally not equal to g(f(x)).

Step by step

1. 1Identify inner and outerIn f(g(x)), g is inner, f is outer.
2. 2Evaluate innerCompute g(x) or g(value).
3. 3Plug into outerSubstitute the result into f.