Chapter 1.2, Problem 6QR

Solution

To find: all the values of $x$ algebraically for which the expression is not defined and show it graphically.

  $x=\{-4,4\}$

Given Information:

Consider the inequality $\frac{x}{x^2-16}$ .

Concept used:

The denominator of the algebraic expression will be undefined for any value of $x$ where the denominator equals to 0.

Calculation:

Observe that the function is not defined when $x^2-16=0$ .

Simplify $x^2-16=0$

  $\begin{array}{c}{x}^2-16=0\\ x^2-4^2=0\\ x=4,-4\end{array}$

Therefore, the algebraic expression is not defined at $x=\{-4,4\}$ .

  

Plot the graph to show the expression is not defined graphically also.

It is observed from the graph that the graph has two asymptotes at $x=4,x=-4$ .

Therefore, the algebraic expression and the graph is not defined at $x=\{-4,4\}$ .