question_answer

Let \[f(x)=15-\left| x-10 \right|;x\in R.\]Then the set of all values of x, at which the function, \[g\left( x \right)=\left( \left( x \right) \right)\] is not differentiable, is : [JEE Main 9-4-2019 Morning]

A) {5, 10, 15, 20}           

B) {10, 15}

C) {5, 10, 15}

D) {10}

Correct Answer: C

Solution :

 \[f\left( x \right)=15-|x-10|,x\in R\]           \[f\left( f(x \right))=15-|f(x)-10|\]           \[=15-|15-x|x-10|-10|\]           \[=15-|5-|x-10||\] \[x=5,10,15\]are points of non differentiability Aliter : At \[x=10\left( x \right)\] is non differentiable also, when \[15\left| x10 \right|=10\]\[\Rightarrow x=5,15\] \[\therefore \]non differentiability points are \[\left\{ 5,10,15 \right\}\]