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

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Answer 1 · 2015-10-02T19:33:06

The function is even.

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

The domain of #f# is #RR-{0}#

For any #x# in the domain, #-x# is also in the domain and:

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

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

# = f(x)#

So #f# is even.

We have used #(-x)^4 = x^4# and

#(-x)^-4 = 1/(-x)^4 = 1/x^4=x^-4#.