Let f\left ( x \right )=15-\left | x-10 \right |;x\epsilon \textbf{R}. Then the set of all values of x, at which the function ,g\left ( x \right )=f\left ( f\left ( x \right ) \right ) is not differentiable, is :

  • Option 1)

    \left \{ 5,10,15 \right \}         

  • Option 2)

    \left \{ 10,15 \right \}

  • Option 3)

     \left \{ 5,10,15 ,20\right \}

  • Option 4)

    \left \{ 10 \right \}

 

Answers (1)

f\left ( x \right )=15-\left | x-10 \right |

g\left ( x \right )=f\left ( f\left ( x \right ) \right )=f\left ( 15-\left | x-10 \right | \right )

          =15-\left | 5-\left | x-10 \right | \right |

          =\left\{\begin{matrix} 15-\left | x-5 \right | & x< 10\\ 15-\left | 15-x \right | & 10< x \end{matrix}\right.

         =\left\{\begin{matrix} 10+x & x< 5\\ 20-x &5< x10 \\ x& 10< x< 15\\ 30-x & 15< x \end{matrix}\right.

   f\left ( x \right ) is not differentiable at

        x=5,10,15


Option 1)

\left \{ 5,10,15 \right \}         

Option 2)

\left \{ 10,15 \right \}

Option 3)

 \left \{ 5,10,15 ,20\right \}

Option 4)

\left \{ 10 \right \}

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions