Question

The domain of the function \( f(x) = \sqrt{x - 3 + 4\sqrt{5 - x}} \) is

• A. \( [1,2] \)
• B. \( [2,4] \)
• C. \( [3,5] \)
• D. \( [3,20] \)
• E. \( [12,20] \)

Hint:

For multiple square roots, take intersection of all conditions.

Answer 1

The Correct Option is C

Concept: For square roots, expression inside must be non-negative.

Step 1: Apply conditions.
\[ x-3 \ge 0 \Rightarrow x \ge 3 \] \[ 5-x \ge 0 \Rightarrow x \le 5 \]

Step 2: Combine.
\[ 3 \le x \le 5 \]