The domain of definition of f x -4 x - x 2 isA- R -0-4B- R -0-4-C- 0-4D- -0-4-

The correct option is D [0, 4] Given: f(x) = √(4x x^2) Clearly, f(x) assumes real values if 4x x^2 ≥ 0 ⇒ x(4 x) ≥ 0 ⇒ x(x 4) ≥ 0 ⇒ x(x 4) ≤ 0 ⇒ x ϵ [0, 4] ...

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Standard XII

Mathematics

Domain

The domain of...

Question

The domain of definition of $f (x) = \sqrt{4 x - x^{2}}$ is

R - [0, 4]

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R - (0, 4)

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(0, 4)

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[0, 4]

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Solution

The correct option is D
[0, 4]

Given:
$f (x) = \sqrt{4 x - x^{2}}$
Clearly, f(x) assumes real values if
$4 x - x^{2} \geq 0 \Rightarrow x (4 - x) \geq 0 \Rightarrow - x (x - 4) \geq 0 \Rightarrow x (x - 4) \leq 0 \Rightarrow x ϵ [0, 4]$
Hence, domain (f) = [0, 4]

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Similar questions

Q. The domain of definition of

f (x) = \sqrt{4 x - x^{2}}

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The possible values of $x^{2} + 4$ lie in the interval

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F (x) = \frac{x^{2} - 4 x}{x + 2} [0, 4]

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The domain of definition of f(x)=√4x−x2 is

The correct option is D [0, 4] Given: f(x)=√4x−x2 Clearly, f(x) assumes real values if 4x−x2≥0⇒x(4−x)≥0⇒−x(x−4)≥0⇒x(x−4)≤0⇒xϵ[0,4] Hence, domain (f) = [0, 4]

The domain of definition of $f (x) = \sqrt{4 x - x^{2}}$ is

The correct option is D
[0, 4]

Given:
$f (x) = \sqrt{4 x - x^{2}}$
Clearly, f(x) assumes real values if
$4 x - x^{2} \geq 0 \Rightarrow x (4 - x) \geq 0 \Rightarrow - x (x - 4) \geq 0 \Rightarrow x (x - 4) \leq 0 \Rightarrow x ϵ [0, 4]$
Hence, domain (f) = [0, 4]