Question

The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{3-x}\) is ...

• A. \([0,\infty )\)
• B. \(R\)
• C. \([1,3]\)
• D. \([2,2]\)

Hint:

Both square roots need non-negative inputs.

Answer 1

The Correct Option is C

Step 1: Test points
$x=0$ makes $\sqrt{x-1}$ undefined. $x=4$ makes $\sqrt{3-x}$ undefined. $x=2$ works, and so do $1$ and $3$. The domain is $[1,3]$.

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]