AP EAMCET · Maths · Inverse Trigonometric Functions
If \(f(x)=2+\left|\operatorname{Sin}^{-1} x\right|\) and \(A=\left\{x \in R / f^1(x)\right.\) exists \(\}\), then \(A=\)
- A \(\{0\}\)
- B \([-1,1]\)
- C \((-\infty,-1) \cup(1, \infty)\)
- D \((-1,0) \cup(0,1)\)
Answer & Solution
Correct Answer
(D) \((-1,0) \cup(0,1)\)
Step-by-step Solution
Detailed explanation
\(f(x) = 2 + |\operatorname{Sin}^{-1} x|\) is differentiable when \(\operatorname{Sin}^{-1} x \neq 0\) and \(x \in (-1, 1)\). \(\operatorname{Sin}^{-1} x = 0 \implies x = 0\). \(f(x)\) is not differentiable at \(x=0\) (due to the absolute value) and at \(x=\pm 1\) (due to the…
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