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  • Answer please! - Limit , continuity and differentiability - JEE Main-16

 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)

best_answer

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 \}

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