Question

let a function f:R--->R have just one point of discontinuity and assume only rational values.what kind of discontinuity point must that be?​

Answer 1

The function f : R → R having a single point discontinuity, the type of discointuity point that is possible is:

• Jump Discontinuity: In this type of discontinuity, both one-sided limits exist at the point of discontinuity, but have different values.
• Infinite Discontinuity: This type of discontinuity has both one-sided limits equal to infinity.
• Mixed: In this type of discontinuity, at least one of the one-sided limits does not exist.
• Removable discontinuity: For this type of discontinuity the limit of the discontinuity point exists but is not equal to a value.
• Endpoint Discontinuity: In this type of discontinuity, a single one-sided limit exists.