Answer: The answer is (b) all integers.
Step-by-step explanation: The given function is
[tex]f(x)=4[x-3]+2.[/tex]
We are to check at what points, the graph of the above given function is discontinuous.
Since we all dealing with greatest integer function [x], we must know its definition. It is defined as follows.
For all real numbers, x, the greatest integer function, [x] gives the largest integer less than or equal to x.
Therefore, for all the real numbers x, [x - 3] will give an integer. That is, whatever value of 'x' real we take, we will get the value of f(x) an integer. So, at the integral points [x - 3], the graph will be discontinuous.
Thus, the correct option is (b) all integers.
