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TS EAMCET · Maths · Continuity and Differentiability

The set of all values of \(x\) for which \(f(x)=||x|-1|\) is differentiable is

  1. A \(\{-1,1\}\)
  2. B \(\mathbb{R}-\{-1,1,0\}\)
  3. C \(\mathbb{R}\)
  4. D \((0, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathbb{R}-\{-1,1,0\}\)

Step-by-step Solution

Detailed explanation

\(f(x) = \begin{cases} |x+1| & \text{if } x \(f(x)\) is not differentiable at \(x=-1\) (from \(|x+1|\)). \(f(x)\) is not differentiable at \(x=1\) (from \(|x-1|\)). At \(x=0\): \(f'(0^-) = \frac{d}{dx}(x+1)|_{x=0} = 1\).…