WBJEE · Maths · Continuity and Differentiability
Let \(f(x)=\left\{\begin{array}{cc}x+1, & -1 \leq x \leq 0 \\ -x, & 0 \leq x \leq 1\end{array}\right.\)
- A \(f(x)\) is discontinuous in \([-1,1]\) and so has no maximum value or minimum value in \([-1,1]\)
- B \(f(x)\) is continuous in \([-1,1]\) and so has maximum value and minimum value
- C \(f(x)\) is discontinuous in \([-1,1]\) but still has the maximum and minimum value
- D \(f(x)\) is bounded in \([-1,1]\) and does not attain maximum or minimum value
Answer & Solution
Correct Answer
(C) \(f(x)\) is discontinuous in \([-1,1]\) but still has the maximum and minimum value
Step-by-step Solution
Detailed explanation
Hint : \(f(x)= \begin{cases}x+1 & -1 \leq x \leq 0 \\ -x & 0 obviously \(f(x)\) has local maximum at \(x=0\)
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