If a function is not continuous at a point, then it is not defined at that point. State true/false.
We will use the concept of limit, continuity, and differentiability in order to find true/false.
Answer: False.
Let us see how we will use the concept of limit, continuity, and differentiability in order to find true/false.
Explanation:
If a function is not continuous at some point, then it is not necessary the given point is not in the domain of the function. This is one reason for discontinuity that any point is not in the domain of the function and the point lies within the boundaries of the function. Example: ln x is discontinuous at x = 0.
The second reason for discontinuity can be that the value of the function at that point is different from its left-hand limit and right-hand limit. Example: [x] or greatest integer function is discontinuous at many points but its domain is real number R.
In the above image, we can see that graph is discontinuous as x = 1 but it has a value of y = 1, and hence, the graph is defined as x = 1 which proves our assertion.