A function is even if f(-x) = f(x)
A function is odd if -f(x) = f(-x)
Now, h(-x) = f(-x)g(-x)
Now g(x) is odd, so g(-x) = -g(x)
Now f(x) is even so f(-x) = f(x) ...
so h(-x) = ...
I need to write a proof showing that h(x) is either odd, even, or neither.
Assume h(x) = f(x)*g(x) and f(x) is even and g(x) is odd.
I think the first step would be substituting as follows: h(x)=f(-x)*-g(x) because of the def'n of even and odd functions.
This is where I am stuck and don't know how to proceed.
Any help is appreciated
A function is even if f(-x) = f(x)
A function is odd if -f(x) = f(-x)
Now, h(-x) = f(-x)g(-x)
Now g(x) is odd, so g(-x) = -g(x)
Now f(x) is even so f(-x) = f(x) ...
so h(-x) = ...