How do you know if #f(x) = 13x^4 – 2x^3 + 7x# is an even or odd function?

1 Answer
Nov 14, 2015

#f(x)# is neither even nor odd.

Explanation:

A function #f(x)# is even if #f(-x) = f(x)#
A function #f(x)# is odd if #f(-x) = -f(x)#

To see which (if any) is the case here, we simply look at #f(-x)#.

#f(-x) = 13(-x)^4 - 2(-x)^3 + 7(-x) = 13x^4 + 2x^3 - 7x#

As #f(x) = 13x^4 - 2x^3 +7x#
and #-f(x) = -13x^4 + 2x^3 -7x#

we have that
#f(-x) != f(x)# and #f(-x) != -f(x)#

So #f(x)# is neither even nor odd.