# Composite Function

### Composite Function

If function $$f:X \mapsto Y$$,
and function $$g:Y \mapsto Z$$,
hence, composite function $$gf:X \mapsto Z$$

Example:
If, $$f:x \mapsto 2x + 5$$ and $$g{\rm{ }}:x \mapsto {x^2} - 1$$, find $$gf(2)$$
Answer: $f(x)=2x+5 f(2)=2(2)+5=9$ $gf(2)=g[f(2)]=g(9)$ $g(x)= x 2 −1 gf(2)=g(9)= 9 2 −1=80$