If f(x) = x + 5 and g(x) = x + 5, what is (f - g)(x)?

Correct answer: 0

The governing concept is pointwise subtraction of functions. For every value of x in the common domain, (f − g)(x) is defined as f(x) − g(x). Since the two given functions are identical, substitute their expressions: (f − g)(x) = (x + 5) − (x + 5). Removing the parentheses gives x + 5 − x − 5, and like terms cancel to produce 0. Thus the difference is the zero function and option A is correct. Option B would be obtained by adding the functions, option C merely repeats one original function, and option D has no basis in the subtraction. The result is zero for every permissible x, not just for one particular input.