Question

Where is the graph of f(x)=4[x-3]+2 discontinued?

Answer 1

Answer: The answer is (b) all integers.

Step-by-step explanation: The given function is

`f(x)=4[x-3]+2.`

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.