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The Domain of Definition of F ( X ) = √ 4 X − X 2 is (A) R − [0, 4] (B) R − (0, 4) (C) (0, 4) (D) [0, 4] - Mathematics

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प्रश्न

The domain of definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

विकल्प

  • (a) R − [0, 4]

  • (b) R − (0, 4)

  • (c) (0, 4)

  • (d) [0, 4]

     
MCQ

उत्तर

(d) [0, 4]

Given: 
\[f\left( x \right) = \sqrt{4x - x^2}\]
Clearly, f (x) assumes real values if 4xx2 ≥ 0
⇒ x(4 - x) ≥ 0
 ⇒ -x(x -4) ≥ 0
⇒ x(x -4) ≤ 0
⇒ x ∈ [0, 4]
Hence, domain (f )= [0, 4].
 
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अध्याय 3: Functions - Exercise 3.6 [पृष्ठ ४५]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.6 | Q 37 | पृष्ठ ४५

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