How do you determine if #1/(x^3+1)# is an even or odd function?

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Answer 1 · 2016-04-05T22:54:05

Evaluate #f(2)# and #f(-2)# to show that it is neither.

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

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

In our example, let #f(x) = 1/(x^3+1)#

We find:

#f(2) = 1/(8+1) = 1/9#

#f(-2) = 1/(-8+1) = 1/-7 = -1/7#

So neither #f(-x) = f(x)# for any #x#, nor #f(-x) = -f(x)# for any #x#.

So this function is neither even nor odd.