JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If the domain of the function \( f(x)=\cos^{-1}(\frac{2x-5}{11-3x})+\sin^{-1}(2x^{2}-3x+1) \) is the interval \( [\alpha,\beta] \), then \( \alpha+2\beta \) is equal to:
- A 1
- B 3
- C 5
- D 2
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\( f(x)=\cos^{-1}(\frac{2x-5}{11-3x})+\sin^{-1}(2x^{2}-3x+1) \) \( -1\le\frac{2x-5}{11-3x}\le1 \) \( -1\le2x^{2}-3x+1\le1 \) \( 2x^{2}-3x+2\ge0 \), \( 2x^2 - 3x \le 0 \) \( x\in[0,\frac{3}{2}] \) ....(i) \( \frac{2x-5}{11-3x}+1\ge0 \) \( \frac{2x-5}{11-3x}-1\le0 \)…
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