Chapter 1.2, Problem 27E

To determine

To check: Whether the function $y=\frac{x^3}{x^2-1}$ is even, odd or neither.

Answer to Problem 27E

The function $y=\frac{x^3}{x^2-1}$ s odd function.

Explanation of Solution

Given information: The function is $y=\frac{x^3}{x^2-1}$.

Rewrite the function.

  $\begin{array}{l}y=\frac{x^3}{x^2-1}\\ y=\frac{x^3}{x^2-1x^0}\end{array}$

The function $y=\frac{x^3}{x^2-1}$ is the quotient of odd powers of $x$ to the even power of $x$ . So, it satisfies the property of odd function that is $f\left(-x\right)=-f\left(x\right)$.

Therefore, the function $y=\frac{x^3}{x^2-1}$ is odd function.