SOLUTION: Hi, I have a problem that says if F and G are both even and h(x)=(f*g)(x), prove that h(x) is also even. It's pretty self-explanatory, so i don't know how i'm supposed to show wor

Question 55129: Hi,
I have a problem that says if F and G are both even and h(x)=(f*g)(x), prove that h(x) is also even. It's pretty self-explanatory, so i don't know how i'm supposed to show work for it. thanks
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
h(x) = f(x)*g(x)
Let us find out whether h(x) is even.
Now, h(-x) = f(-x)g(-x).
Now, f(x) and g(x) are even so f(-x) = f(x) and g(-x) = g(x).
Hence, h(-x) = f(x)g(x) = h(x).
So h(x) is an even function.
NB: The proposition is also true when f(x) and g(x) are both odd functions.
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