Question

The set of points where f(x) = x – [x] not differentiable is ____________.

Answer 1

Let g(x) = x and h(x) = [x].

Every polynomial function is differentiable for all x ∈ R. So, g(x) = x is differentiable for all x ∈ R.

Also, the function h(x) = [x] is discontinuous at all integral values of x i.e. x ∈ Z. So, h(x) = [x] is not differentiable at all integral values of x i.e. x ∈ Z.

Now, f(x) = g(x) − h(x) = x − [x]

So, the function f(x) = x − [x] is differentiable for all x ∈ R except at all integral values of x i.e. x ∈ Z. The function f(x) = x − [x] is not differentiable for all x ∈ R − Z.

Thus, the set of points where f(x) = x – [x] not differentiable is R − Z.


The set of points where f(x) = x – [x] not differentiable is ___R − Z___.