Functions.md (1037B)
1 +++ 2 title = 'Functions' 3 template = 'page-math.html' 4 +++ 5 # Functions 6 Function f: A ➝ B — binary relation f of type A × B such that every x ∈ A relates to at most one y ∈ B 7 8 - domain: all possible input values 9 - domain of definition: all input values that actually produce defined output 10 - codomain: what could be the output of a function (like “integers” with f(x)=2x) 11 - range/image: what actually is the output of a function (like “even numbers” with f(x)=2x) 12 13 injective: if each element x of domain maps to at most one element y of codomain (“one-to-one”) 14 15 surjective: if each element x of domain maps to at least one element y of codomain; the range is the codomain (“onto”) 16 17 total: if the function is defined for all possible input values (domain) 18 19 bijective: if the function is total, injective, and surjective 20 21 22 ## Composition: 23 (g o f) of f: A ➝ B and g: B ➝ C 24 25 - $D_{g \circ f} \subseteq D_f$ 26 - $R_{g \circ f} \subseteq R_g$ 27 28 ## Inverse: 29 a function has an inverse only if it’s injective (one-to-one)