The domain of the function fX-3-2x-21-x-sin -1 x isA- -0-1- -1-0- -1-2-D- -1-2- 1-

The correct option is A [0, 1]sin^ 1x ≥ 0 ⇒ 0 ≤ x ≤ 1 and 2^x +2^1 x≤ 3 ⇒ 2^x+2.2^ x 3 ≤ 0 Put 2^x=t, then t^2 3t+2 ≤ 0 ⇒ (t 2)(t 1) ≤ 0 ⇒ 1 ≤ t ≤ 2 i.e 1 ≤ 2^ ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

The domain of...

Question

The domain of the function $f (X) = \sqrt{3 - 2^{x} - 2^{1 - x}} + \sqrt{s i n^{- 1} x}$ is

[-1, 0]

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[0, 1]

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

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[1,2]

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Solution

The correct option is B [0, 1]
$s i n^{- 1} x \geq 0 \Rightarrow 0 \leq x \leq 1$
and $2^{x} + 2^{1 - x} \leq 3 \Rightarrow 2^{x} + {2.2}^{- x} - 3 \leq 0$
Put $2^{x} = t$ , then $t^{2} - 3 t + 2 \leq 0 \Rightarrow (t - 2) (t - 1) \leq 0$
$\Rightarrow 1 \leq t \leq 2$ i.e $1 \leq 2^{x} \leq 2$
$\Rightarrow 0 \leq x \leq 1$

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