The domain of the real function fx-3-2x-21-x-sin -1 x is

The correct option is B [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^x ...

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Standard XII

Mathematics

Real Valued Functions

The domain of...

Question

The domain of the real 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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The domain of the real function f(x)=√3−2x−21−x+√sin−1x is

The correct option is B [0,1] sin−1x≥0⇒0≤x≤1 and 2x+21−x≤3⇒2x+2.2−x−3≤0 Put 2x=t,then t2−3t+2≤0⇒(t−2)(t−1)≤0 ⇒1≤t≤2 i.e., 1≤2x≤2 ⇒0≤x≤1

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