Chapter 14.3, Problem 71AYU

To determine

To find: The numbers at which $f$ is continuous.

Answer to Problem 71AYU

Continuous for all real values of $x$ excluding $x\le 0$.

Interval of continuity: $\left(0,\infty \right)$.

Explanation of Solution

Given:

$f\left(x\right)=\frac{x-3}{\text{ln}x}$

Calculation:

$f\left(x\right)=\frac{x-3}{\text{ln}x}$

The denominator function $\text{ln}x$ is defined only for $x>0$.

Since $f\left(x\right)=\frac{x-3}{\text{ln}x}$ is undefined for $x\le 0$; therefore $f\left(x\right)=\frac{x-3}{\text{ln}x}$ is continuous for all real numbers excluding $x\le 0$.

Thus the interval on which $f$ is continuous is $\left(0,\infty \right)$.