Question

Let f(x) = | |x| - 1|, then points where f(x), is not differentiable is/are

(a) 0, ±1

(b) ± 1

(c) 0

(d) 1

Answer 1

Correct option (a) 0, ±1

Explanation :

Using graphical transformation.

As, we know the function is not differentiable at sharp edges and in figure (iii)

In function,

y = | |x| - 1| , we have 3 sharp edges at x = - 1, 0, 1.

Hence, f(x) is not differentiable at {0, ±1}.