Question

define the set of all points where the function f(X) =X/1+|X|​

Answer 1

Explanation:

The 1st one is by checking the left hand derivative and right hand Derivative and if they are equal then the function is differentiable..

And second method by checking the Differentiability at some point so if u take x=1,2,3,-1,-2… the function will have some value and that means the f(x) is defined and if the function becomes infinite or undefined then there must be a critical point (and we always know that at critical point the function is non differentiable) but as there is no critical point so f (x) will be defined in this case x can take any value i.e. x belongs to all Real no. And the value of y will always be positive and u can also check by the graph that there is no sharp point in the graph and hence always differentiable at all points..