Show that this odd/even property is true

A-R-Q · **Joined:** Sat, 20 Nov 2010 21:17:02 UTC **Posts:** 432

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.
//

Justin · **Joined:** Wed, 21 May 2003 04:27:18 UTC **Posts:** 995

Looks fine to me...that may be the only way to prove the result!

Shadow · **Posted:** Sat, 10 Sep 2011 07:41:42 UTC

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.

Justin · **Joined:** Wed, 21 May 2003 04:27:18 UTC **Posts:** 995

Shadow wrote:

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. :roll:

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Show that this odd/even property is true

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