Domain of f (x) = √ {{{log }₂}left( {frac{{10x - 4}}{{4 - {x^2}}}} right) - 1} , is

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1.Relation and Function

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Domain of $f (x)$ = $\sqrt {{{\log }_2}\left( {\frac{{10x - 4}}{{4 - {x^2}}}} \right) - 1} $ , is

A

$\left[ { - 6, - 2} \right) \cup \left[ {1,2} \right)$

B

$\left[ { - 6,2} \right)$

C

$\left[ { - 6,1} \right)$

D

$\left( { - 2,2} \right)$

Solution

$\log _{2}\left(\frac{10 x-4}{4-x^{2}}\right) \geq 1$

$\Rightarrow \frac{10 x-4}{4-x^{2}}-2 \geq 0 $

$\Rightarrow \frac{x^{2}+5 x-6}{4-x^{2}} \geq 0$

$\Rightarrow \frac{(x+6)(x-1)}{(x-2)(x+2)} \leq 0$

Standard 12

Mathematics

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