Precalc0105to0107-page38

Precalc0105to0107-page38 - (Section 1.7: Symmetry...

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(Section 1.7: Symmetry Revisited) 1.7.8 Example 7 (Proving a Quotient Rule) Prove: even () odd = odd . That is, prove that, if a (nontrivial) even function is divided by a (nontrivial) odd function, the resulting function is odd . § Solution • Let f be an even function, and let g be an odd function. Let h = f g . • Let D = Dom f ± Dom g ² ³ ´ µ \ x ± gx = 0 {} . Then, D = Dom h . • Because f is even on D , ± x ² D , f ± x = fx . • Because g is odd on
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This document was uploaded on 12/29/2011.

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