Is #f(x)=-3x^4-2x -5# odd, even, or neither?

Question

1819 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-23T00:20:02

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

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

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

In this case, we have

#f(-x) = -3(-x)^4 - 2(-x) - 5#

#=-3x^4 +2x -5#

#!= f(x)#

Thus #f(x)# is not even. Additionally

#-f(x) = -(-3x^4 -2x - 5)#

#=3x^4+2x+5#

#!= f(-x)#

Thus #f(x)# is not odd. Therefore, #f(x)# is neither even nor odd.