CUET · MATHS · PYQ PAPER 2023
The function \(f: R \rightarrow R\) given by \(f(x)=-|x-1|\) is
- A continuous as well as differentiable at \(x=1\)
- B not continuous but differentiable at \(x=1\)
- C continuous but not differentiable at \(x=1\)
- D neither continuous nor differentiable at \(x=1\)
Answer & Solution
Correct Answer
(C) continuous but not differentiable at \(x=1\)
Step-by-step Solution
Detailed explanation
\(f(1) = -|1-1| = 0\) \(\lim_{x \to 1^-} f(x) = \lim_{x \to 1^-} -(-(x-1)) = \lim_{x \to 1^-} (x-1) = 0\) \(\lim_{x \to 1^+} f(x) = \lim_{x \to 1^+} -(x-1) = 0\) \(f(1) = \lim_{x \to 1} f(x) \implies\) continuous at \(x=1\).…
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