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JEE Main20204 Sep 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

The function f x = π 4 + tan - 1 x , x ≤ 1 1 2 x - 1 , x > 1 is :

Options

  1. Acontinuous on R - 1 and differentiable on R - - 1 , 1 .
  2. Bboth continuous and differentiable on R - 1
  3. Ccontinuous on R - - 1 and differentiable on R - - 1 , 1
  4. Dboth continuous and differentiable on R - - 1

Correct answer

A. continuous on R - 1 and differentiable on R - - 1 , 1 .

Step-by-step solution

f x = π 4 + tan - 1 x , x ≤ 1 1 2 x - 1 , x > 1 Making graph Clearly, function is continuous on R – 1 and differentiable on R – – 1 , 1 .

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