fx=3-2x-21-x+sin-1xDomain and range of sine inverse is-1≤x≤1 and -π2≤sin-1x≤π2Since quantity inside square root should be non-negativesin-1x≥0⇒0≤sin-1x≤π20≤x≤1 Also3-2x-21-x≥03-2x-22x≥0Let 2x=t, t>03-t-2t≥03t-t2-2t≥03t-t2-2≥0t2-3t+2≤0t2-2t-t+2≤0tt-2-t-2≤0t-2t-1≤0Solution of x-ax-b≤0, where a<b is given by x∈a,bt∈1,22x∈1,21≤2x≤2log2 1≤log2 2x≤log2 20≤x≤1Therefore domain of functionn will be x∈0, 1

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Solve this: 3. tÜnain of the furwtion t (x) 11 3-2' -21 • + •'sin (D) (0, 11

f (x) = \sqrt{3 - 2^{x} - 2^{1 - x}} + \sqrt{\sin^{- 1} x} D o m a i n a n d r a n g e o f \sin e i n v e r s e i s - 1 \leq x \leq 1 a n d - \frac{π}{2} \leq \sin^{- 1} x \leq \frac{π}{2} S i n c e q u a n t i t y i n s i d e s q u a r e r o o t s h o u l d b e n o n - n e g a t i v e \sin^{- 1} x \geq 0 \Rightarrow 0 \leq \sin^{- 1} x \leq \frac{π}{2} 0 \leq x \leq 1

A l s o 3 - 2^{x} - 2^{1 - x} \geq 0 3 - 2^{x} - \frac{2}{2^{x}} \geq 0 L e t 2^{x} = t, t > 0 3 - t - \frac{2}{t} \geq 0 \frac{3 t - t^{2} - 2}{t} \geq 0 3 t - t^{2} - 2 \geq 0 t^{2} - 3 t + 2 \leq 0 t^{2} - 2 t - t + 2 \leq 0 t (t - 2) - (t - 2) \leq 0 (t - 2) (t - 1) \leq 0 S o l u t i o n o f (x - a) (x - b) \leq 0, w h e r e a < b i s g i v e n b y x \in [a, b] t \in [1, 2] 2^{x} \in [1, 2] 1 \leq 2^{x} \leq 2 \log_{2} 1 \leq \log_{2} 2^{x} \leq \log_{2} 2 0 \leq x \leq 1 T h e r e f o r e d o m a i n o f f u n c t i o n n w i l l b e x \in [0, 1]

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Solve this: Solve this: 3. tÜnain of the furwtion t (x) 11 3-2' -21 • + •'sin (D) (0, 11

Solve this:

Solve this: 3. tÜnain of the furwtion t (x) 11 3-2' -21 • + •'sin (D) (0, 11