Hi there,
I am having a little trouble with one question regarding Functions (Even, Odd, Neither). I am unsure how I would approach it, as no specific function is given.
The question is as follows:
Show that;
E(x)=21(f(x)+f(−x))is an even function.
I thought that I may be able to assume
f(x) is even, as otherwise the function of
E(x) would not be even.
Therefore, as
f(x) is even;
f(x)=f(−x),
and Therefore:
E(x)=21(f(x)+f(x))E(x)=21(2f(x))E(x)=f(x)Therefore, since
f(x) is even,
E(x) must also be, given they are equal to one another.
This may be completely wrong so any help would be greatly appreciated,
Thanks in advance,