Function \(F\) from set \(A\) to set \(B\) is a kind of #202204282024 with domain \(A\) and co-domain \(B\) that satisfies two properties:
- For every element of \(x\) in \(A\), there is an element \(y\) of \(B\) such that \((x, y) \in F\). (\(x\) and \(y\) must in the domain and co-domain respectively where \(x\) is the first element of the ordered pair of \(F\), and every \(x\) must be related to at least one of the element in co-domain)
- For all elements \(x\) in \(A\) and \(y\) and \(z\) in \(B\), if \((x, y) \in F\) and \((x, z) \in F\) then \(y = z\). (\(x\) has only one related element in the co-domain)
Based on this definition, the unique element in \(B\) related to \(x\) by \(F\) is denoted \(F(x)\), read “F of x”. We can understand it as \(F(x)\) is the output or result of input \(x\) in the function \(F\). A function could be express in 202204281700 as \(F = \{(x, y) \in A \times B|y = F(x)\}\). (relation is a 202204281535 of 202204281601 of \(A\) and \(B\))
Two function is equal, that is \(f = g\), if and only if, \(f(x) = g(x)\) for every \(x\) in set \(A\).