Discussion
The domain of the function \(f(x) = \sqrt{x - 3} + 4\sqrt{5 - x}\) is
Answer: C
The domain is [3,5].
Each square root needs a non-negative argument: \(x - 3 \geq 0\) gives \(x \geq 3\), and \(5 - x \geq 0\) gives \(x \leq 5\). Both hold together on \(3 \leq x \leq 5\). The coefficient 4 in front of the second root does not affect the domain.
[3,20] and [12,20] come from wrongly multiplying the 5 by 4; [1,2] and [2,4] include points below 3 where \(\sqrt{x - 3}\) is not real.
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