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 Post subject: Show that this odd/even property is truePosted: Sat, 10 Sep 2011 03:06:19 UTC
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Joined: Sat, 20 Nov 2010 21:17:02 UTC
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Show that:
(i) The product of two even functions is an even one.

Attempt: I was skeptical as to whether or not my attempt is a proper way of answering this question:

Quote:
Let g(x) and f(x) be even functions.
By definition, a function is even if f(-x) = f(x)

Let h(x) = f(x)*g(x)
h(x) = f(x)*g(x)
h(-x) = f(-x)*g(-x)
= f(x)*g(x) , by the Definition of Even Functions
= h(x)

Therefore, the product of 2 even functions is an even one.
//

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 Post subject: Re: Show that this odd/even property is truePosted: Sat, 10 Sep 2011 04:33:59 UTC
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Joined: Wed, 21 May 2003 04:27:18 UTC
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Looks fine to me...that may be the only way to prove the result!

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)

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 Post subject: Re: Show that this odd/even property is truePosted: Sat, 10 Sep 2011 07:41:42 UTC
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Justin wrote:
Looks fine to me...that may be the only way to prove the result!

It's never a good idea to say "the only way" (unless you're dealing with one of those "the axiom of choice is equivalent to X" statements). I think this is probably the simplest and best ways to do it however.

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 Post subject: Re: Show that this odd/even property is truePosted: Sat, 10 Sep 2011 07:52:07 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 21 May 2003 04:27:18 UTC
Posts: 995
Justin wrote:
Looks fine to me...that may be the only way to prove the result!

It's never a good idea to say "the only way" (unless you're dealing with one of those "the axiom of choice is equivalent to X" statements). I think this is probably the simplest and best ways to do it however.

Fair enough, since we are mincing words here, I'll say "the only way barring an extremely clever and unnecessarily complicated proof that the margin is too small to contain" a la Fermat.

_________________
"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)

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