The range of the function f x -9- x 2 isA- 0-3B- -0-3- 0-3-D- -0-3

The correct option is B [0,3]Given that f(x)=√(9 x^2) The domain of the given function is x∈[ 3,3] ⇒ 3≤ x≤3 ⇒ 0≤ x^2≤9 ⇒ 9≤ x^2≤0 ⇒ 0≤ 9 x^2≤9 ⇒ 0≤√(9 x^2)≤ ...

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Standard XII

Mathematics

Sign of Quadratic Expression

The range of ...

Question

The range of the function $f (x) = \sqrt{9 - x^{2}}$ is

(0, 3)

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[0, 3]

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(0, 3]

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[0, 3)

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Solution

The correct option is B $[0, 3]$
Given that $f (x) = \sqrt{9 - x^{2}}$
The domain of the given function is $x \in [- 3, 3]$
$\Rightarrow - 3 \leq x \leq 3$
$\Rightarrow 0 \leq x^{2} \leq 9$
$\Rightarrow - 9 \leq - x^{2} \leq 0$
$\Rightarrow 0 \leq 9 - x^{2} \leq 9$
$\Rightarrow 0 \leq \sqrt{9 - x^{2}} \leq 3$
$\Rightarrow 0 \leq f (x) \leq 3$

The range of the function is $[0, 3]$ .

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The range of the function f(x)=√9−x2 is

The correct option is B [0,3]Given that f(x)=√9−x2 The domain of the given function is x∈[−3,3] ⇒−3≤x≤3 ⇒0≤x2≤9 ⇒−9≤−x2≤0 ⇒0≤9−x2≤9 ⇒0≤√9−x2≤3 ⇒0≤f(x)≤3 The range of the function is [0,3].

The range of the function $f (x) = \sqrt{9 - x^{2}}$ is