Find the domain of the function $f(x)=\frac{1}{x-5}$.

Step-by-step solution

1. 1. The denominator cannot be zero; otherwise the function is undefined.
2. 2. Set $x-5\ne 0\to x\ne 5$.
3. 3. Thus the domain is $\mathbb{R}\setminus \{5\}$.

Concept tested: Domain of a rational function

Published 4 October 2026 · How this solution was prepared and checked