Question

The function f(x) = [x] is continuous at
(a) 4
(b) –2
(c) 1
(d) 1.5

Answer 1

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).