InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Statement-1: The function `f(x)=[x]+x^(2)` is discontinuous at all integer points. Statement-2: The function g(x)=[x] has Z as the set of points of its discontinuous from left.A. 1B. 2C. 3D. 4 |
|
Answer» Correct Answer - A Let k be an integer. Then, `underset(x to k^(-))lim g(x)=k-1 and g(k)=k Rightarrow underset(x to k^(-))lim g(x) ne g(k)` So, k is a point of left discontinuity of g. Hence, the points of discontinuous from left of function g is the set Z of all integers. So, statement-2 is true. We have `f(x)={{:(,k-1+x^(2),"if "k-1 le x lt k),(,k+x^(2),"if "k le x lt k+1):}` Clearly, f(x) is discontinuous at all integers points as g(x)=[x] is discontinuous there at. |
|