QJEEM19Mac538: JEE Main 2019 Mathematics - Class 12 JEEM19Mac538 Solution: Let ƒ(x) = 15 –

ƒ(x) = 15 – |x – 10|

g(x) = ƒ(ƒ(x)) = 15 – |ƒ(x) – 10|

= 15 – |15 – |x – 10| – 10|

= 15 – |5 – |x – 10||

As this is a linear expression so it is non differentiable when value inside the modulus is zero.

So non differentiable when

x – 10 = 0 $\Rightarrow$ x = 10

and 5 – |x – 10| = 0

$\Rightarrow$ |x – 10| = 5

$\Rightarrow$ x - 10 = $\pm$ 5

$\Rightarrow$ x = 5, 15

$\therefore$ g(x) is not differentiable at x = 5, 10, 15.