Precalc0105to0107-page24

Precalc0105to0107-page24 - (Section 1.6: Combining...

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(Section 1.6: Combining Functions) 1.6.12 PART E: “DECOMPOSING” COMPOSITE FUNCTIONS Example 8 (“Decomposing” a Composite Function) Find component functions f and g such that f ± g () x = 3 x + 1 . We want to “decompose” f ± g . • Neither f nor g may be an identity function. For example, do not use: gx = x and fu = 3 u + 1 . This would not truly be a decomposition. f does all the work! x ± g : = x ± x , our u ±² ³´ ³ ± f : = 3 u + 1 f µ g ³³³³³³³³³ ´ ³³³³³³³³³ ± 3 x + 1 fgx ² ³ ´ µ · ³ § Solution • We need: = 3 x + 1 . • We can think of f and g as buttons we are designing on a basic calculator. We need to set up f and g so that, if x is an initial input to Dom f ± g , and
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This document was uploaded on 12/29/2011.

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