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Question: Answered & Verified by Expert
Let [t] denote the greatest integer less than or equal to t.
Let f(x)=x-[x], g(x)=1-x+[x], and h(x)=min{f(x),g(x)},x[-2,2]. Then h is :
MathematicsContinuity and DifferentiabilityJEE MainJEE Main 2021 (26 Aug Shift 2)
Options:
  • A continuous in [-2,2] but not differentiable at more than four points in (-2,2)
  • B Continous in [-2,2] but not differentiable at exactly three poionts in (-2,2)
  • C not continuous at exactly four points in [-2,2]
  • D not continuous at exactly three points in [-2,2]
Solution:
2304 Upvotes Verified Answer
The correct answer is: continuous in [-2,2] but not differentiable at more than four points in (-2,2)

f(x)=x-[x]={x}

g(x)=1-x+[x]=1-{x}

Now, Graph of min {f(x),g(x)}

Clearly graph is continuous in [-2,2] but non differentiable at 7 points (i.e. greater than 4) in (-2,2)

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