For functions, even means f(-x)=f(x) and odd means f(-x)=-f(x)
[tex]\sqrt{x^2} - 9[/tex]
The only occurrence of x is squared so this is even.
[tex]|x-3|[/tex]
This isn't even or odd, it's neither. f(1)=|1-3|=2. f(-1)=|-1-3|=4 for example.
[tex]f(x) = \dfrac{x}{x^2-1}[/tex]
This one is odd because
[tex]f(-x) = \dfrac{-x}{(-x)^2-1} = -\dfrac{x}{x^2-1} = -f(x)[/tex]
[tex]g(x)=x+x^2[/tex]
g(1)=1+1=2
g(-1)=-1+1=0
neither odd nor even
