A function [tex]f(x)[/tex] is even if [tex]f(-x)=f(x)[/tex], and is odd if [tex]f(-x)=-f(x)[/tex].
Example:
[tex]f(x)=x^2[/tex] is even, since [tex]f(-x)=(-x)^2=x^2=f(x)[/tex].
[tex]g(x)=x^3-x[/tex] is odd, since [tex]g(-x)=(-x)^3-(-x)=-x^3+x=-(x^3-x)=-g(x)[/tex].
