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Question
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
Options
(a) [1, ∞)
(b) (−∞, 3)
(c) (1, 3)
(d) [1, 3]
MCQ
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Solution
(d) [1, 3]
\[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\]
\[\text{ For f(x) to be defined, } \]
\[\left( x - 1 \right) \geq 0\]
\[ \Rightarrow x \geq 1 . . . (1)\]
\[\text{ and } \left( 3 - x \right) \geq 0\]
\[ \Rightarrow 3 \leq x . . . (2)\]
\[\text{ From (1) and (2), } \]
\[x \in [1, 3]\]
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