Question:
The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{3-x}\) is ...
The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{3-x}\) is ...
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Both square roots need non-negative inputs.
Updated On: Oct 1, 2026
- \([0,\infty )\)
- \(R\)
- \([1,3]\)
- \([2,2]\)
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The Correct Option is C
Solution and Explanation
Step 1: Conditions
\(x-1\ge0\) gives \(x\ge1\), and \(3-x\ge0\) gives \(x\le3\).
Step 2: Intersect
Both hold together only for \(1\le x\le3\), so the domain is \([1,3]\). Option (C).
Final Answer:
The domain is \([1,3]\), option (C). \[ \boxed{\text{(C) } [1,3]} \]
\(x-1\ge0\) gives \(x\ge1\), and \(3-x\ge0\) gives \(x\le3\).
Step 2: Intersect
Both hold together only for \(1\le x\le3\), so the domain is \([1,3]\). Option (C).
Final Answer:
The domain is \([1,3]\), option (C). \[ \boxed{\text{(C) } [1,3]} \]
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