JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Let \([\cdot]\) denote the greatest integer function. If the domain of the function \(f(x) = \sin^{-1}\left(\dfrac{x+[x]}{3}\right)\) is \([\alpha, \beta)\), then \(\alpha^2 + \beta^2\) is equal to:
- A \(2\)
- B \(5\)
- C \(10\)
- D \(13\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
For the function \(f(x) = \sin^{-1}\left(\dfrac{x+[x]}{3}\right)\) to be defined, the argument of the inverse sine function must lie in the interval \([-1, 1]\). \(-1 \le \dfrac{x+[x]}{3} \le 1\) \(-3 \le x + [x] \le 3\) Using the fractional part function \(\{x\}\), we can write…
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