MHT CET · Maths · Differentiation
The domain of the derivative of the functions \(f(x)\left\{\begin{array}{cc}\tan ^{-1} x, & \text { if }|x| \leq 1 \ \frac{1}{2}(|x|-1), & \text { if }|x|>1\end{array}\right.\) is given by
- A \(R-\{1\}\)
- B \(R-\{0\}\)
- C \(R-\{-1,1\}\)
- D \(R-\{-1\}\)
Answer & Solution
Correct Answer
(C) \(R-\{-1,1\}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x) \begin{cases}\frac{1}{2}(-x-1) & x<-1 \\ \tan ^{-1} x & -1 \leq x \leq 1 \\ \frac{1}{2}(x-1) & x>1\end{cases} \\ & \Rightarrow f^{\prime}(x) \begin{cases}-\frac{1}{2} & x<-1 \\ \frac{1}{1+x^2} & -1 < x < 1 \\="" \frac{1}{2}="" &="" x="">1\end{cases} \end{aligned}\)
\(\because f(x)\) discontinuous at \(x=-1\) and \(x=1\)
Hence \(f(x)\) is not differentiable at \(x=-1\) and \(x=1\)
\(\because f(x)\) discontinuous at \(x=-1\) and \(x=1\)
Hence \(f(x)\) is not differentiable at \(x=-1\) and \(x=1\)
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