Precalc0105to0107-page18

Precalc0105to0107-page18 - (Section 1.6: Combining...

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(Section 1.6: Combining Functions) 1.6.6 PART D: COMPOSITION OF FUNCTIONS We compose functions when we apply them in sequence , as we did in Section 1.4 on transformations. Let f and g be functions. The composite function f ± g is defined by: f ± g () x = fgx Its domain is x ± ± x ± Dom g and gx ± Dom f {} . • The domain consists of the “legal” inputs to g that yield outputs that are “legal” inputs to f . x ± g ± ± f f ± g ²³ ´´´´´ µ ´´´´´ ± Think of f ± g as a “merged” function. WARNING 5 : The function f ± g applies g first and then f . Think of pressing a g button on a basic calculator followed by an
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