TS EAMCET · Maths · Inverse Trigonometric Functions
The domain of the derivative of the function \(f(x)=\operatorname{Cos}^{-1}(2 x-5)-\operatorname{Sin}^{-1}(x-2)\) is
- A \([2,3]\)
- B \((-\infty, 2] \cup[3, \infty)\)
- C \((-\infty, 2) \cup(3, \infty)\)
- D \((2,3)\)
Answer & Solution
Correct Answer
(D) \((2,3)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{-2}{\sqrt{1-(2x-5)^2}} - \frac{1}{\sqrt{1-(x-2)^2}}\) \(1-(2x-5)^2 > 0 \implies (2x-5)^2 \(-1 \(1-(x-2)^2 > 0 \implies (x-2)^2 \(-1 \(\text{Domain} = (2,3) \cap (1,3) = (2,3)\)
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