Chapter 3.1, Problem 20E

To determine

To find: whether graph of $g\left(x\right)$ is symmetric with respect to origin, and explain the reason

Answer to Problem 20E

Symmetric

Explanation of Solution

Given information:

  $g\left(x\right)=\frac{x^2-1}{x}$

Calculation:

Let’s check whether $g\left(-x\right)$ is equal to $-g\left(x\right)$ or not by substituting replacing x with $-x$ as shown below.

$g\left(x\right)=\frac{x^2-1}{x}$
Value of $g\left(-x\right)$	Value of $-g\left(x\right)$
$\begin{array}{c}g\left(-x\right)=\frac{{\left(-x\right)}^2-1}{-x}\\ =\frac{-x^2+1}{x}\end{array}$	$\begin{array}{c}-g\left(x\right)=-\left(\frac{x^2-1}{x}\right)\\ =\frac{-x^2+1}{x}\end{array}$

Since, $g\left(-x\right)$ is equal to $-g\left(x\right)$ . Thus the graph is symmetric to the origin.