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MHT CET202015 Oct 2020Morning ShiftMathematicsContinuity and DifferentiabilityActual

If aligned f(x) &= |x-2| x-2 , for x 2 &=1 , for x=2, aligned then which of the following statements is true?

Options

  1. Af(x) is continuous at x=2
  2. B_ x 2⁻ f(x)=f(2)
  3. C_ x 2⁺ f(x)= _ x 2⁻ f(x)
  4. Df(x) is discontinuous at x=2

Correct answer

D. f(x) is discontinuous at x=2

Step-by-step solution

Here aligned |x-2| &=x-2, if x>2 _ x 2⁻ f(x)= _ x 2⁺ f(x)=0 &=-(x-2), if x < 2 aligned But f(2)=1 0 So f(x) is discontinuous at x=2

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