Question

Determine whether the ffunction X/(x^2-1) is odd even or neither

Answer 1

equation is:

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

so if its even f(-x) should be equal to f(x)

that means

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

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)

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

so as we can see f(-x)= - f(x)

so the function is odd

Ans:function is odd and not even