Is the function $f (x) = \frac{1}{x^{3} + 1}$ $f(x)=1/(x^3+1)$ even, odd or neither?

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Is the function $f (x) = \frac{1}{x^{3} + 1}$ $f(x)=1/(x^3+1)$ even, odd or neither?

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Answer 1 · 2018-05-07T17:52:28

It is neither .

Explanation:

A function f(x) is even if f(-x)=f(x) and odd if f(-x)=-f(x)
Putting x=-x we get
f(x)= $\frac{1}{- x^{3} + 1}$ $1/(-x^3+1)$
which is not equal to either f(x) or f(-x).
So its neither of the two.

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Is the function $f (x) = \frac{1}{x^{3} + 1}$ $f(x)=1/(x^3+1)$ even, odd or neither?

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