Home/Differential Calculus/Notation, functions and domains/Composition and inverseSection 1.3Composition and inverseFormulaCopy LaTeX(f∘g)(x)=f(g(x))(f\circ g)(x)=f(g(x))(f∘g)(x)=f(g(x))Function composition; requires x∈Dom(g)x\in\operatorname{Dom}(g)x∈Dom(g) and g(x)∈Dom(f)g(x)\in\operatorname{Dom}(f)g(x)∈Dom(f).View detail →FormulaCopy LaTeXf(f−1(y))=y,f−1(f(x))=xf(f^{-1}(y))=y,\qquad f^{-1}(f(x))=xf(f−1(y))=y,f−1(f(x))=xIdentities of a bijective function and its inverse on their respective domains.f−1(f(x))=xf^{-1}(f(x))=xf−1(f(x))=xView detail →
FormulaCopy LaTeX(f∘g)(x)=f(g(x))(f\circ g)(x)=f(g(x))(f∘g)(x)=f(g(x))Function composition; requires x∈Dom(g)x\in\operatorname{Dom}(g)x∈Dom(g) and g(x)∈Dom(f)g(x)\in\operatorname{Dom}(f)g(x)∈Dom(f).View detail →
FormulaCopy LaTeXf(f−1(y))=y,f−1(f(x))=xf(f^{-1}(y))=y,\qquad f^{-1}(f(x))=xf(f−1(y))=y,f−1(f(x))=xIdentities of a bijective function and its inverse on their respective domains.f−1(f(x))=xf^{-1}(f(x))=xf−1(f(x))=xView detail →