To understand the given function f(x) = x [x], let's break it down into two parts:

1. The function [x] represents the greatest integer function, also known as the floor function. It returns the greatest integer less than or equal to x. For example, [2.5] = 2 and [3] = 3.

2. The function x [x] is the product of x and [x]. Therefore, if we substitute a value of x, let's say x = 2.5, then f(2.5) = 2.5 [2.5] = 2.5 * 2 = 5.

Now, let's analyze the options given:

a) all x in I
This option states that the function f(x) = 1 for all x in the set of integers. However, this is not true because the function f(x) = x [x] is a continuous function and takes different values for different values of x.

c) all x in R
This option states that the function f(x) = 1 for all x in the set of real numbers. Again, this is not true because the function f(x) = x [x] takes different values for different values of x.

d) all x in R - {0}
This option states that the function f(x) = 1 for all x in the set of real numbers except 0. However, this is also not true because the function f(x) = x [x] takes different values for different values of x.

Therefore, the correct option is:

b) all x in R
This option states that the function f(x) = 1 for all x in the set of real numbers. This is true because the function f(x) = x [x] takes different values for different values of x, including the case where it equals 1.

In conclusion, the correct answer is option 'B' - all x in R.