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Question
The domain of definition of \[f\left( x \right) = \sqrt{4x - x^2}\] is
Options
(a) R − [0, 4]
(b) R − (0, 4)
(c) (0, 4)
(d) [0, 4]
MCQ
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Solution
(d) [0, 4]
Given:
\[f\left( x \right) = \sqrt{4x - x^2}\]
Clearly, f (x) assumes real values if 4x - x2 ≥ 0
⇒ x(4 - x) ≥ 0
⇒ x(4 - x) ≥ 0
⇒ -x(x -4) ≥ 0
⇒ x(x -4) ≤ 0
⇒ x ∈ [0, 4]
Hence, domain (f )= [0, 4].
⇒ x(x -4) ≤ 0
⇒ x ∈ [0, 4]
Hence, domain (f )= [0, 4].
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