Answer
$f(x)=\dfrac{1}{x-5}$ is continuous for all real numbers except for $5$.
(Other answers are possible.)
Work Step by Step
Take the function:
$f(x)=\dfrac{1}{x-5}$
When the denominator is $0$, then the fraction $f(x)=\dfrac{1}{x-5}$ is undefined. By the zero product rule, we have: $x-5 \ne 0$ . So, $x\ne 5$ .
The fraction function is continuous everywhere, except for where it is undefined. So, $f(x)=\dfrac{1}{x-5}$ is continuous for all real numbers except for $5$.
