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)

S solutionqc

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

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

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

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

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

$f\left ( x \right )$ 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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Let Then the set of all values of at which the function , is not differentiable, is : Option 1) Option 2) Option 3) Option 4)

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