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NDA2016MathematicsContinuity and DifferentiabilityActual

Let f: A R , where A=R 0 is such that f(x)= x+|x| x . On which one of the following sets is f(x) continuous?

Options

  1. AA
  2. BB= x R: x 0
  3. CC= x R: x 0
  4. DD = R

Correct answer

A. A

Step-by-step solution

For x 0f(x)= x+x x =2 For x 0 aligned & f(x)= x-x x =0 & _ x 0⁺ f(x)=2 & _ x 0⁻ f(x)=0 & f(0)=2 aligned It is discontinuous at x=0 . Option (a) is correct.

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