Functions:Operations

Operations

Functions obey many of the same operations as normal numbers. However, one key difference is the domain of the function, which may change depending on the operator.

List of Operations for Functions

Name	Notation	Domain
Addition	$(f+g)(x)=f(x)+g(x)$	domain f ∩ domain g
Subtraction	$(f-g)(x)=f(x)-g(x)$	domain f ∩ domain g
Product	$(f\cdot g)(x)=f(x)\cdot g(x)$	domain f ∪ domain g
Division	$\left({\dfrac {f}{g}}\right)(x)={\dfrac {f(x)}{g(x)}}$	domain f ∪ domain g \ {a : g(a) = 0}
Composition	$f\circ g(x)=f(g(x))$	domain g ∪ {g(x) : f(g(x)) ∈ domain f}

Resources

• Functions, Wikibooks: Real Analysis