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JEE Main20199 Apr 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f x = 15 – x – 10 ; x ∈ R . Then the set of all values of x , at which the function g x = f ( f x ) is not differentiable, is:

Options

  1. A5 , 10 , 15
  2. B10
  3. C10 , 15
  4. D5 , 10 , 15 , 20

Correct answer

A. 5 , 10 , 15

Step-by-step solution

f x = 15 - x - 10 ⇒ g x = f f x ⇒ g x = 15 - f x - 10 = 15 - 15 - x - 10 - 10 = 15 - 5 - x - 10 = 15 - x - 10 - 5 We know that, x =       x , x ≥ 0 - x , x < 0 Case 1 : When x < 10 g x = 15 - 10 - x - 5 ⇒ g ( x ) = 15 - 5 - x Now if x < 5 , then g x = 15 - 5 + x = x + 10 And if x ≥ 5 , then g ( x ) = 15 + 5 - x = 20 - x Case 2 : x ≥ 10 g x = 15 - x - 10 - 5 ⇒ g ( x ) = 15 - x - 15 Now if 10 ≤ x < 15 ⇒ g x = 15 - 15 + x So, g x = x

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