Find the domain of the function $f(x)=\sqrt{5-2x}$.

Step-by-step solution

1. The radicand in a square root must be non‑negative.
2. Set $5-2x\ge 0$ and solve: $-2x\ge -5$ gives $x\le \frac{5}{2}$.
3. All real numbers less than or equal to $\frac{5}{2}$ satisfy the condition.
4. Thus the domain is $(-\infty ,\frac{5}{2}]$.

Concept tested: Domain of a square‑root function

Published 13 October 2026 · How this solution was prepared and checked