Question

Determine algebraically whether the function

$f\left(x\right)=\frac{5x}{x^2-9}$is even, odd, or neither.

Short answer

The given function is odd

Step-by-step solution

Given information

We are given an equation$f\left(x\right)=\frac{5x}{x^2-9}$

Substitute -x in the above equation

We get

$$\begin{gathered} f\left(x\right)=\frac{5x}{x^2-9} \\ f(-x)=\frac{-5x}{x^2-9} \\ f(-x)=-f\left(x\right) \end{gathered}$$

Hence the given function is a odd function