Composition of Functions
Definition 1. Let f:X⟶Y and g:Y⟶Z be functions. The composition of f and g is the function g∘f:X⟶Z where (g∘f)(x)=f(g(x)),∀x∈X. In other words, g∘f={(x,z)∈X×Z|∃y∈Y such that (x,y)∈f∧(y,z)∈g}.
Definition 1. Let f:X⟶Y and g:Y⟶Z be functions. The composition of f and g is the function g∘f:X⟶Z where (g∘f)(x)=f(g(x)),∀x∈X. In other words, g∘f={(x,z)∈X×Z|∃y∈Y such that (x,y)∈f∧(y,z)∈g}.