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

Question

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, { 10 }, { 10 , 15 }, { 5 , 10 , 15 , 20 }, { 5 , 10 , 15 }

MARKS App · Accepted Answer

​ f ( x ) = 15 − ∣ x − 10∣ ⇒ f ( f ( x )) = f ( 15 − ∣ x − 10∣ ) = 15 − ∣15 − ∣ x − 10∣ − 10∣ = 15 − ∣5 − ∣ x − 10∣∣ ​ graph has 3 corner points x = 5 , x = 10 and x = 15 So, it is not differentiable at x ∈ { 5 , 10 , 15 }

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