AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.7 Composition of Functions
Notes
$(f\circ g)(x)=f(g(x))$: apply $g$ first, then $f$.
- Order matters: usually $f(g(x))\ne g(f(x))$.
- Domain: inputs where $g$ works and $g(x)$ is in $f$'s domain.
Practice
$f(x)=x^2$, $g(x)=x+1$. $f(g(2))=$
$g(2)=3$, $f(3)=9$.
Using the same functions, $g(f(2))=$
$f(2)=4$, $g(4)=5$.
$f(g(x))$ means:
Inside first.
Ready for more? Take the Unit 2 test.