Thread: Mathematics Odd/Even Functions

My mathematics book is very poor on it's explinations, so can someone look at my logic and tell me if I understand this correctly. I'm looking for a yes or no.

Code:

  f(x)=x^3 - x
 
   f(-x)=(-x)^3 - (-x)
 
	=(-1)^3 (x)^3 + x
 
	=(-1)(x)^3 + x // since f(x) != f(-x) then not even
 
	=(-x)^3 + x
 
	=(-1)(x^3 - x) //odd
 
	=-f(x)
 
f(-x) = -f(x) Odd