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Function composition
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==Examples== [[File:Example for a composition of two functions.svg|thumb|Concrete example for the composition of two functions.]] * Composition of functions on a finite [[set (mathematics)|set]]: If {{math|1=''f'' = {(1, 1), (2, 3), (3, 1), (4, 2)} }}, and {{math|1=''g'' = {(1, 2), (2, 3), (3, 1), (4, 2)} }}, then {{math|1=''g'' β ''f'' = {(1, 2), (2, 1), (3, 2), (4, 3)} }}, as shown in the figure. * Composition of functions on an [[infinite set]]: If {{math|''f'': '''R''' β '''R'''}} (where {{math|'''R'''}} is the set of all [[real number]]s) is given by {{math|1=''f''(''x'') = 2''x'' + 4}} and {{math|''g'': '''R''' β '''R'''}} is given by {{math|1=''g''(''x'') = ''x''<sup>3</sup>}}, then: {{block indent|text={{math|1=(''f'' β ''g'')(''x'') = ''f''(''g''(''x'')) = ''f''(''x''<sup>3</sup>) = 2''x''<sup>3</sup> + 4}}, and}} {{block indent|text={{math|1=(''g'' β ''f'')(''x'') = ''g''(''f''(''x'')) = ''g''(2''x'' + 4) = (2''x'' + 4)<sup>3</sup>}}.}} * If an airplane's altitude at time {{mvar|t}} is {{math|''a''(''t'')}}, and the air pressure at altitude {{mvar|x}} is {{math|''p''(''x'')}}, then {{math|(''p'' β ''a'')(''t'')}} is the pressure around the plane at time {{mvar|t}}. * Function defined on finite sets which change the order of their elements such as [[permutation]]s can be composed on the same set, this being composition of permutations.
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