If f(x) = x − 2 and g(x) = x − 2, what is (f − g)(x)?

Correct answer: 0

The difference of two functions is defined pointwise: (f − g)(x) = f(x) − g(x). Since the two given functions are exactly identical, substitute their expressions to obtain (x − 2) − (x − 2). Removing the brackets gives x − 2 − x + 2, and combining like terms gives 0 for every value of x in their common domain. Thus the difference is the zero function, so option A is correct. Option B results from subtracting the constants incorrectly, option C is the square of x − 2 rather than a difference, and option D simply repeats one function without performing the subtraction. Equality of the two functions is the decisive observation.