Is the function #g(x) = x^3-5x# even, odd or neither?

1 Answer
Sep 25, 2015

Answer:

Rather than using a particular number or numbers, the best method is to substitute #-x# and simplify.

Explanation:

To determine whether #g# if even, odd, or neither, evaluate #g(-x)#.

If #g(-x)# simplifies to #g(x)#, then #g# is even. If #g(-x)# simplifies to an equivalent to #-g(x)#, then #g# is odd. It may be neither even nor odd.

#g(x) = x^3-5x#

#g(-x) = (-x)^3-5(-x)#

# = -x^3+5x#

# = -(x^3-5x)#

# = -g(x)#.

So, #g# is odd.