Question
Question: The number of points at which the function f(x) =\(\frac{1}{x - \lbrack x\rbrack}\) ([.] denotes, th...
The number of points at which the function f(x) =x−[x]1 ([.] denotes, the greatest integer function) is not continuous is
A
1
B
2
C
3
D
None of these
Answer
None of these
Explanation
Solution
x– [x] = 0 when x is an integer,
so that, f(x) is discontinuous for all x ∈ I. i.e.
f(x) is discontinuous at infinite number of points