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Example 1 Find each of the following functions, and state its domain.

Example 1 Find each of the following functions, and state its domain. (a) FoG (b) GoF Solution (a) The composite function ( FoG )( x ) is obtained by substituting G(x) for x in the formula of F(x) .

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Example 1 Find each of the following functions, and state its domain.

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  1. Example 1 Find each of the following functions, and state its domain. (a) FoG (b) GoF Solution(a) The composite function (FoG)(x) is obtained by substituting G(x) for x in the formula of F(x). The domain of FoG is the domain of G which consists of all numbers except –5/8 where the denominator of G(x) vanishes, i.e. the domain of FoG is (-,-5/8)  (-5/8, ) . (b) The composite function (GoF)(x) is obtained by substituting F(x) for x in the formula of G(x). The domain of GoF is the domain of F which is . Observe that FoG and GoF are different functions – they have different domains and different formulas.

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