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	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f-g)(x) = f(x) - g(x)}	domain f ∩ domain g
Product	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f \cdot g)(x) = f(x) \cdot g(x)}	domain f ∪ domain g
Division	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left( \dfrac{f}{g} \right)(x) = \dfrac{f(x)}{g(x)}}	domain f ∪ domain g \ {a : g(a) = 0}
Composition	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f \circ g(x) = f(g(x))}	domain g ∪ {g(x) : f(g(x)) ∈ domain f}

Resources

• Functions, Wikibooks: Real Analysis