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anonymous
 one year ago
Show that if f and g are even functions, then f+g and f times g are even.
anonymous
 one year ago
Show that if f and g are even functions, then f+g and f times g are even.

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\text{ we are given } f(x)=f(x) \text{ and } g(x)=g(x) \\ \text{ \let's call the \sum of } f \text{ and } g , h \\ h(x)=f(x)+g(x) \] plug in x

freckles
 one year ago
Best ResponseYou've already chosen the best response.1We are trying to see if h(x)=h(x) and if so h is even

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i can just show your way and it proves that its even??

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if you show h(x)=h(x) you are done

freckles
 one year ago
Best ResponseYou've already chosen the best response.1have you replace x with x in h(x)=f(x)+g(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and then use that f(x)=f(x) and g(x)=g(x)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok 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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