Explanation:

To find the values of f(x) for different values of x, let's consider two cases:

Case 1: x ≥ 2
In this case, the function f(x) can be written as f(x) = |x - 2|.
When x is greater than or equal to 2, the expression inside the absolute value bars, x - 2, is positive or zero. Therefore, f(x) = x - 2.

Case 2: x < />
In this case, the function f(x) can be written as f(x) = |x - 2|.
When x is less than 2, the expression inside the absolute value bars, x - 2, is negative. Therefore, f(x) = -(x - 2) = -x + 2.

So, the function f(x) can be defined as follows:
f(x) = x - 2, when x ≥ 2
f(x) = -x + 2, when x < />

Now, let's analyze the given options:

a) f(x) = (f(x))^2:
This option states that f(x) is equal to the square of f(x). However, since f(x) can take different values depending on the range of x, it is not always true that f(x) is equal to (f(x))^2. Hence, option a) is not always true.

b) f(x) = f(x):
This option states that f(x) is equal to f(x). This is obviously true for any function, so option b) is always true.

c) f(x) = x - 2:
This option states that f(x) is equal to x - 2. However, as mentioned earlier, f(x) can take different values depending on the range of x. When x is greater than or equal to 2, f(x) is indeed equal to x - 2. But when x is less than 2, f(x) is equal to -x + 2. Therefore, option c) is not always true.

d) None of these:
Based on the analysis above, we can conclude that none of the given options are always true. Hence, option d) is the correct answer.