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JEE Main202116 Mar 2021Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let the functions f : R → R and g : R → R be defined as : f x = x + 2 , x < 0 x 2 , x ≥ 0 and g x = x 3 , x < 1 3 x - 2 , x ≥ 1 Then, the number of points in R where f o g x is NOT differentiable is equal to :

Options

  1. A3
  2. B1
  3. C0
  4. D2

Correct answer

B. 1

Step-by-step solution

f g x = g x + 2 ,   g x < 0 g x 2 ,   g x ≥ 0 = x 3 + 2 , x < 0 x 6 , x ∈ [ 0 , 1 ) 3 x - 2 2 , x ∈ [ 1 , ∞ ) f o g x ' = 3 x 2 , x < 0 6 x 5 , x ∈ [ 0 , 1 ) 2 3 x - 2 × 3 , x ∈ [ 1 , ∞ ) At x = 0 L . H . L . ≠ R . H . L . (Discontinuous) At x = 1 L . H . L . = R . H . L . (continuous) L . H . D . = 6 = R . H . D . ⇒ f o g x is differentiable for all x ∈ R - 0

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