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NDA2017MathematicsContinuity and DifferentiabilityActual

Let f( x ) be defined as follows : f(x)= cases 2 x +1, & -3 x -2 x -1, & -2 x 0 x +2, & 0 x 1 cases Which one of the following statements is correct in respect of the above function?

Options

  1. AIt is discontinuous at x =-2 but continuous at every other point.
  2. BIt is discontinuous at x =-2 but continuous at every other point.
  3. CIt is discontinuous at x =0 but continuous at every other point.
  4. DIt is discontinuous at every point.

Correct answer

C. It is discontinuous at x =0 but continuous at every other point.

Step-by-step solution

f(x)= array cc 2 x+1, & -3 x -2 x-1, & -2 x 0 x+2, & 0 x 1 array . Here, f (0⁻ )=-1 and f (0⁺ )=2 So, f ( x ) is discontinuous at x =0 and continuous at other points.

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