Question

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

• A. {5,10,15,20}
• B. {10,15}
• C. {5,10,15}
• D. {10}

Answer 1

Answer: (C)

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