Chapter 1.1, Problem 48E

To determine

To find: domain of $f\left(x\right)=\frac{3x}{x^2-5}$

Answer to Problem 48E

  $\left\{x|x\ne \sqrt{5}\right\}$

Explanation of Solution

Given information:

The function, $f\left(x\right)=\frac{3x}{x^2-5}$

Calculation:

For $f\left(x\right)$ , the denominator should not be zero. Put the denominator equivalent to 0 and evaluate the value of x as shown below.

  $\begin{array}{c}{x}^2-5=0\\ x^2=5\left(\text{Adding 5 to both sides}\right)\\ x=\sqrt{5}\left(\text{Taking square roots on both sides}\right)\end{array}$

The denominator of function $f\left(x\right)$ will be zero at $x=\sqrt{5}$ . So, this will not be in the domain.

Hence, the domain will be $\left\{x|x\ne \sqrt{5}\right\}$ .