anonymous
  • anonymous
Show that if f and g are even functions, then f+g and f times g are even.
Mathematics
katieb
  • katieb
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freckles
  • freckles
\[\text{ we are given } f(x)=f(-x) \text{ and } g(x)=g(-x) \\ \text{ \let's call the \sum of } f \text{ and } g , h \\ h(x)=f(x)+g(x) \] plug in -x
freckles
  • freckles
We are trying to see if h(x)=h(-x) and if so h is even
anonymous
  • anonymous
so i can just show your way and it proves that its even??

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freckles
  • freckles
if you show h(x)=h(-x) you are done
freckles
  • freckles
have you replace x with -x in h(x)=f(x)+g(x)
freckles
  • freckles
and then use that f(-x)=f(x) and g(-x)=g(x)?
anonymous
  • anonymous
yes
freckles
  • freckles
ok you can try showing v(x)=f(x)*g(x) is also even replace x with -x again and use the fact that f and g are even to see if v(x)=v(-x)

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