JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Let \([\cdot]\) denote the greatest integer function. If the domain of the function \(f(x) = \cos^{-1}\left(\dfrac{4x+2[x]}{3}\right)\) is \([\alpha, \beta]\), then \(12(\alpha + \beta)\) is equal to:
- A \(6\)
- B \(8\)
- C \(9\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
For the domain of \(f(x) = \cos^{-1}\left(\dfrac{4x+2[x]}{3}\right)\), the argument must satisfy: \(-1 \le \dfrac{4x+2[x]}{3} \le 1\) \(-3 \le 4x + 2[x] \le 3\) Let \(x = I + f\), where \(I = [x] \in \mathbb{Z}\) and \(f = \{x\} \in [0, 1)\). Substituting \(x = I + f\) into the…
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