These are the options for the Question: The function f(x) = [x], where [a] denotes the greatest integer less than or equal to x, is continuous at
(a) x=1
(b) x = 1.5
(c) x=-2
(d) x=4
The correct answer is –
The function f(x) = [x] is continuous for all values of x except for integers, where it has jump discontinuities. At integer values, the function changes value suddenly by 1.
Therefore, the function f(x) = [x] is continuous at all values of x except for integers.
Answer: None of the options (a), (b), (c), or (d) are correct.
