Composite Functions (HSC SSCE Mathematics Advanced): Flashcards

Output of one function becomes input of second function

Function composition

$g$ is applied first, then $f$

Work from the inside out

Order matters; $f(g(x))$ and $g(f(x))$ usually differ

Substitution method

Domain of $f(x)$ and that $f(x)$ outputs are valid for $g$

Range of $g(x)$, restricted by output of $f(x)$

Outputs from $g$ are inputs for $f$

Apply $g$ first, then apply $f$ to the result