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Unformatted text preview: g 1 ( ) = g 1 ( ) or g 1 ( ) = g 1 ( ) , that would not have been enough to prove that g was even or odd. Examples cannot prove that a function g is even or odd, unless Dom g ( ) is a finite set. g is neither even nor odd. Let f be a (nontrivial) even function, and let g be a (nontrivial) odd function. Then, f + g and f g must be neither even nor odd. (Experiment with graphs and numbers. See the Exercises.) Example 6 (Revisiting Example 5) Let g t ( ) = t 3 + t + 1 ; this is not g in the box above. Since g t ( ) = 1 ( ) + t 3 + t ( ) , g can take the form even ( ) + odd ( ) , and thus g is neither even nor odd....
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This document was uploaded on 12/29/2011.
- Spring '09