Question:
The function f(x) = [x] is continuous at
(a) 4
(b) $-2$
(c) 1
(d) $1.5$
Solution:
The graph of f(x) = [x] is shown below.
It can be seen that, the function f(x) = [x] is discontinuous at all integral values of x. It is continuous at all points except the integer points.
Thus, the function f(x) = [x] is continuous at x = 1.5 and discontinuous at x = 4, x = –2 and x = 1.
Hence, the correct answer is option (d).