equation is:
[tex] f(x) = \frac{x}{ {x}^{2} - 1 } [/tex]
so if its even f(-x) should be equal to f(x)
that means
[tex]f( - x) = \frac{ - x}{ {( - x)}^{2} - 1} \\ \\ f( - x) = - \frac{ x}{ {x}^{2} - 1} [/tex]
so f(x) is not equal to f(-x) so its not even
If its odd than f(-x) should be equal to -f(x)
[tex] - f(x) = - ( \frac{ x}{ { x}^{2} - 1 } ) \\ - f(x) = - \frac{ x}{ {x}^{2} - 1 } [/tex]
so as we can see f(-x)= - f(x)
so the function is odd
Ans:function is odd and not even
