Range of the function f(x)=log2(4x+2+2−x) is :

f(x)=log2(42+x+2−x);−2≤x≤2 2+x+2−x=y 4+24−x2=y2 y∈[2,22]Range f(x)=[log2422,log242]f (x) lies between [12,1]

Range of the function f(x)=log2(4x+2+2−x) is :

f(x)=log2(42+x+2−x);−2≤x≤2 2+x+2−x=y 4+24−x2=y2 y∈[2,22]Range f(x)=[log2422,log242]f (x) lies between [12,1]

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Range of the function $f (x) = \log_{2} (\frac{4}{\sqrt{x + 2} + \sqrt{2 - x}})$ is :

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$(0, \infty)$

$[\frac{1}{2}, 1]$

$[1, 2]$

$[\frac{1}{4}, 1]$

answer is B.

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Detailed Solution

$f (x) = \log_{2} (\frac{4}{\sqrt{2 + x} + \sqrt{2 - x}}); - 2 \leq x \leq 2$
$\sqrt{2 + x} + \sqrt{2 - x} = y$
$4 + 2 \sqrt{4 - x^{2}} = y^{2}$
$y \in [2, 2 \sqrt{2}]$
Range $f (x) = [\log_{2} \frac{4}{2 \sqrt{2}}, \log_{2} \frac{4}{2}]$
f (x) lies between $[\frac{1}{2}, 1]$