Let f(x) = 15 -- |x -- 10|; x [ ] R.

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 :

Accepted Answer

f(x) = 15 -- |x -- 10|

g(x) = f(f(x)) = 15 -- |f(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.

Solutions · 1