How do you determine if $f (x) = \frac{x}{x^{2} - 1}$ $f(x)= x /( x^2 - 1)$ is an even or odd function?

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Answer 1 · 2016-03-21T20:57:25

Find $f (- x) = - f (x)$ $f(-x) = -f(x)$ , so $f (x)$ $f(x)$ is an odd function.

An even function satisfies: $f (- x) = f (x)$ $f(-x) = f(x)$ for all $x$ $x$ in the domain.

An odd function satisfies: $f (- x) = - f (x)$ $f(-x) = -f(x)$ for all $x$ $x$ in the domain.

In our example we find:

$f (- x) = \frac{- x}{{(- x)}^{2} - 1} = - (\frac{x}{x^{2} - 1}) = - f (x)$ $f(-x) = (-x)/((-x)^2-1) = -(x/(x^2-1)) = -f(x)$

So $f (x)$ $f(x)$ is an odd function.

How do you determine if f(x)= x /( x^2 - 1)f(x)=xx2−1f(x)= x /( x^2 - 1) is an even or odd function?