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

1. 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

2. freckles

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

3. anonymous

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

4. freckles

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

5. freckles

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

6. freckles

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

7. anonymous

yes

8. 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)