Question

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

• A. $\left\{0,5 , 10\right\}$
• B. $\left\{5,10\right\}$
• C. $\left\{0,5 , 10,15\right\}$
• D. $\left\{5,10,15\right\}$

Answer 1

Answer: (A)

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