Could you explain a little bit more on this part please? Thanks.If g is even, then g(-x)= g(x). Now, what can you say of [itex]f\cdot g(-x)= f(g(-x))[/itex]?
NO! f.g(-x)= f(g(-x)) as you say below:Could you explain a little bit more on this part please? Thanks.
f(-x)= f(x)
g(-x)= g(x)
f.g(-x) = f(-x(g(-x)))
and f(g(x))= f.g (x) doesn't it?f.g(-x) = f(g(x))
So you have just said, (f.g)(-x)= f.g(x), haven't you?It is even? Because a function is even if:
f:(-a,a) -> R if for all [tex]x \in (-a,a)[/tex], f(x) = f(-x)
Please help me, I don't know if I'm right.
Regards,
Sorry for the off-topic:and f(g(x))= f.g (x) doesn't it?