EXAMPLE 7 If f x x and g x 1 x find each function and its domain a fog b gof c fof d gog SOLUTION a fog x f g x f The domain of

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EXAMPLE 7 If f x x and g x 1 x find each function and its domain a fog b gof c fof d gog SOLUTION a fog x f g x f The domain of fog is x 1 x 0 x x b For X gof x g f x g x to be defined we must have x 2 Thus we have c fof x f f x The domain of fof is the interval x d gog x g g x This expression is defined when both 1 x 2 and the second is equivalent to 1 x domain of gog is the closed interval which is the interval For 1 x to be defined we must have 1 x 20 that is x 1 or so the domain of gof is the closed interval and 1 1 x or 1 x 1 or x The first inequality means x Thus x so the

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