4. Composition of Functions

Product of Functions Definition:

Given functions f(x) and g(x) we can form their product f g:
(fg)(x) = f(x)g(x)

Example

$f(x)=\sqrt{x}\to Domain:[0,\infty )$ $g(x)=x+2\to Domain:R$ $(fg)(x)=(x+2)\sqrt{x}\to Domain:[0,\infty )$

Composition of Functions Definition:

If f(x) and g(x) are two functions, the composite function f ∘ g is defined by:
(f ∘ g)(x) = f(g(x))

Example

$f(x)=x^2-x$ $g(x)=\sin (x)$ $(f\circ g)(x)=f(g(x))=f(\sin (x))=(\sin (x){)}^2-(\sin (x))$ $(g\circ f)(x)=g(f(x))=g(x^2-x)=\sin (x^2-x)$