The idea

Composite functions

Why fg(x) means "g first, then f", how to chain outputs into inputs for numbers and for algebra, and why the order almost always matters.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

In this lesson — start anywhere

Algebra · Functions

Why fg(x) means "g first, then f", how to chain outputs into inputs for numbers and for algebra, and why the order almost always matters.

The first time an exam prints

fg(x)

it looks like a typo — or a multiplication. It's neither: it is two machines chained, the output of one piped straight into the other.

fg(x) = f\big(g(x)\big)

Take

f(x) = 3x - 4

and

g(x) = x^2 + 1

, and chase a number through each chain, one machine at a time:

fg(2): \quad g(2) = 5, \;\text{then}\; f(5) = 11.

gf(2): \quad f(2) = 2, \;\text{then}\; g(2) = 5.

Keep reading — free

The rest of the explanation, plus 2 worked examples you step through move by move.

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