EPTProve that the product of two odd functions is an even function.
Math Problem T_T
| Blogs > decafchicken |
|
decafchicken
United States20089 Posts
Prove that the product of two odd functions is an even function. | ||
|
BuGzlToOnl
United States5918 Posts
| ||
Kau
Canada3500 Posts
| ||
|
azndsh
United States4447 Posts
definition of even function: f(x) = f(-x) Let your two odd functions be f(x) and g(x). From the definition, we know that f(x) = -f(-x) and g(x) = -g(-x). Then multiply and tada! f(x)g(x) = f(-x)g(-x), so the product is obviously even by definition. | ||
|
azndsh
United States4447 Posts
| ||
|
Kau
Canada3500 Posts
| ||
|
BuGzlToOnl
United States5918 Posts
+ Show Spoiler + T________________T | ||
|
decafchicken
United States20089 Posts
kau are you holykau from scgd? | ||
|
Jonoman92
United States9104 Posts
| ||
|
Kau
Canada3500 Posts
On October 11 2007 10:13 decafchicken wrote: kau are you holykau from scgd? Yessir I am | ||
|
Dark.Carnival
United States5095 Posts
| ||
|
Aphelion
United States2720 Posts
On October 11 2007 10:50 Jonoman92 wrote: Could is be as simple as the concept that any 2 negatives multiplied together will produce a positive answer? Just a guess.... I'm in pre-calc but we don't do proofs we only do those in geometry. Exactly it. let f(x), g(x) = odd functions so f(-x) = -f(x), g(-x) = -g(x) g(-x)f(-x) = (-g(x))(-f(x)) = g(x)f(x) so g(x)f(x) = g(-x)f(-x) By definition, g(x)f(x) is an even function | ||
|
oneofthem
Cayman Islands24199 Posts
| ||
|
azndsh
United States4447 Posts
On October 11 2007 12:43 oneofthem wrote: was in week 3 hw for my real analysis thing. pah. wtf ... week 3 we were on topology man i hated that class | ||
|
YoUr_KiLLeR
United States3420 Posts
of course you'd have to be a lot more formal than that, i just didnt want to type everything out but i think you get the idea. | ||
|
azndsh
United States4447 Posts
On October 11 2007 14:33 YoUr_KiLLeR wrote: i think you could also say that odd functions have an odd degree and even functions have an even degree, so the product of two odd functions will have a degree of (degree of 1st function + degree of 2nd function), and the sum of 2 odd numbers is even, so the product of the two odd functions gets you a function with an even number degree. of course you'd have to be a lot more formal than that, i just didnt want to type everything out but i think you get the idea. that's assuming you have a polynomial function, which isn't necessarily the case -- i.e. sin(x), cos(x) are odd, even respectively (although the terms odd/even function did come from the fact that polynomial functions of odd/even degrees demonstrated those properties) | ||
IntoTheWow
is awesome32277 Posts
| ||
|
YoUr_KiLLeR
United States3420 Posts
On October 11 2007 14:58 azndsh wrote: that's assuming you have a polynomial function, which isn't necessarily the case -- i.e. sin(x), cos(x) are odd, even respectively (although the terms odd/even function did come from the fact that polynomial functions of odd/even degrees demonstrated those properties) oh yea that completely went over my head. | ||
| ||
