Let f(x)=10-|x - 5|,x∈ R , then the set of all values of x at which f(f (x)) is not differentiable is

Question

Let f(x)=10-|x - 5|,x∈ R , then the set of all values of x at which f(f (x)) is not differentiable is (A)  0,5 , 10  (B)  5,10  (C)  0,5 , 10,15  (D)  5,10,15

Tardigrade Admin · Accepted Answer

f(f (x)=10-|f (x) - 5|=10-|10 - |x - 5| - 5| =10-|5 - |x - 5||⇒ 10-||x - 5| - 5| Points where f(f(x)) is non-differentiable are x-5=0 |x - 5|=5 x=5 x=0,10

Q. Let $f (x) = 10 - ∣ x - 5 ∣, x \in R$ , then the set of all values of $x$ at which $f (f (x))$ is not differentiable is

${0, 5, 10}$

${5, 10}$

${0, 5, 10, 15}$

${5, 10, 15}$

$f (f (x) = 10 - ∣ f (x) - 5∣ = 10 - ∣10 - ∣ x - 5∣ - 5∣$
$= 10 - ∣5 - ∣ x - 5∣∣ \Rightarrow 10 - ∣∣ x - 5∣ - 5∣$
Points where $f (f (x))$ is non-differentiable are
$x - 5 = 0$ & $∣ x - 5 ∣ = 5$
$x = 5$ & $x = 0, 10$

Q. Let f(x)=10−∣x−5∣,x∈R , then the set of all values of x at which f(f(x)) is not differentiable is

{0,5,10}

{5,10}

{0,5,10,15}

{5,10,15}