Fundamentholfundamenthol
JEE Main2019Math
Q.

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 :

  1. A

    (10, 15)

  2. B

    {5, 10, 15, 20}

  3. C

    {10}

  4. D

    {5, 10, 15}

Solution

Given f(x) = 15 – |(10 – x)|

f(f(x)) = 15 – ||10 – x| – 5|

Non-differentiable at points where

10 – x = 0 and |10 – x| = 5

x = 10 and x – 10 = ±5

x = 10 and x = 15, 5

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