about functions...?

Question

prove that for every function, we can say:
f(x)=g(x)+h(x)
that g(x) is an even function. it means:
g(-x)=g(x)
and h(x) is an odd function. it means:
h(-x)= -h(-x)

no.I want to prove that every function equals to an odd function plus an even function

Answer 1

say g(x)=2x^2+3x+8
h(x)=x-8
g(x)+h(x)=2x^2+4x=f(x)

2.let f(x)=x^2
f(-x)=(-x)^2=x^2 we say f(x)=x^2 is an even function

3.let f(x)=x^3
f(-x)=(-x)^3=-x^3
f(-x)=-f(x)
we say f(x)=x^3 is an odd function

Answer 2

I don't know if I'm understanding your question. What I understand is you want to know when a function is even or odd?

A even function is if f(-x)= f(x)
I know another and easier way to determine when its even if the exponents of the function are even, the function is even

A odd function is if f(-x)= -f(x)
and if the exponents of the function are odd then its odd

but if the exponents are even and odd then the answer is Neither

give it a try work a few and notice the exponents and your answers

I dont know if I answered your question right
but Good Luck!