Question

Show that if f and g are even functions, then f+g and f times g are even.

Answer 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

Answer 2

We are trying to see if h(x)=h(-x) and if so h is even

Answer 3

so i can just show your way and it proves that its even??

Answer 4

if you show h(x)=h(-x) you are done

Answer 5

have you replace x with -x in h(x)=f(x)+g(x)

Answer 6

and then use that f(-x)=f(x) and g(-x)=g(x)?

Answer 7

yes

Answer 8

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)