JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The function \(f(x)=\left\{\begin{array}{l}\frac{\pi}{4}+\tan ^{-1} x,|x| \leq 1 \\ \frac{1}{2}(|x|-1),|x|>1\end{array}\right.\)
- A continuous on \(R -\{1\}\) and differentiable on \(R-\{-1,1\}\)
- B both continuous and differentiable on \(R-\{-1\}\)
- C continuous on \(R -\{-1\}\) and differentiable on \(R -\{-1,1\}\)
- D both continuous and differentiable on \(R -\{1\}\)
Answer & Solution
Correct Answer
(A) continuous on \(R -\{1\}\) and differentiable on \(R-\{-1,1\}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ccc}\frac{\pi}{4}+\tan ^{-1} x & , & x \in(-\infty,-1] \cup[1, \infty) \\ -\frac{(x+1)}{2} & , & x \in(-1,0] \\ \frac{x-1}{2} & , & x \in(0,1)\end{array}\right.\) for continuity at \(x=-1\) L.H.L. \(=\frac{\pi}{4}-\frac{\pi}{4}=0\) R.H.L. \(=0\) so,…
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