AP DSC School Assistant Math Model Test 1

Concept:A square root function $\sqrt{\text{expression}}$ is defined only when the expression inside (the radicand) is non‑negative (≥ 0). For a sum of two square roots to be real, each radicand must satisfy this condition simultaneously.Explanation:We have $f(x)=\sqrt{x-1}+\sqrt{6-x}$.For the first square root: $x-1 \ge 0 \implies x \ge 1$.For the second square root: $6-x \ge 0 \implies x \le 6$.Both conditions must hold at the same time, so $x$ satisfies $1 \le x \le 6$.Thus the set of all permissible values of $x$ (the domain) is the closed interval from 1 to 6.Answer:$[1,6]$ (Option C).