Chapter A.1, Problem 72AYU

To determine

Which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression.

a. $x=3$   b. $x=\text{ 1}$   c. $x=\text{ 0}$   d. $x=-1$ 

Answer to Problem 72AYU

$x=1$ and $x=-1$.

Explanation of Solution

Given:

$\frac{x^3}{x^2-1}$

Calculation:

The domain of the variable $x$ in the expression $\frac{x^3}{x^2-1}$ is $\left\{x\text{|}x\ne \pm 1\right\}$, since, if $x=\pm 1$, the denominator becomes 0, which is not defined. Hence answer is $x=1$ and $x=-1$.