Question

Let $f\left(x\right)=15-|x-10|;x\in R$. Then the set of all values of $x$, at which the function, $g\left(x\right)=f\left(f\right(x\left)\right)$ is not differentiable is:

• A. $\left\{10\right\}$
• B. $\{10,15\}$
• C. $\{5,10,15\}$
• D. $\{5,10,15,20\}$

Answer 1

The correct option is C $\{5,10,15\}$

$f\left(x\right)=15-|x-10|f\left(f\right(x\left)\right)=15-|f\left(x\right)-10|=15-|15-|x-10|-10|=15-|5-|x-10||$
Hence, points of non-differentiability are: 5, 10 and 15.