What does (f-g)(x) denote?

What does (f-g)(x) denote?

• A. f(x) - g(x)
• B. f(x) + g(x)
• C. f(x) / g(x)
• D. g(x) - f(x)

Answer: (A)

When you see (f - g)(x), think of subtracting the second function from the first, evaluated at the same input. For any x, you calculate f(x) and g(x), then do f(x) minus g(x). The result is a new function whose value at x is the difference of the original outputs. For example, if f(x) = 2x and g(x) = x + 1, then (f - g)(x) = 2x - (x + 1) = x - 1. This is not addition or division; it’s subtraction. Reversing the order would give (g - f)(x) = g(x) - f(x), which generally isn’t the same as (f - g)(x).

When you see (f - g)(x), think of subtracting the second function from the first, evaluated at the same input. For any x, you calculate f(x) and g(x), then do f(x) minus g(x). The result is a new function whose value at x is the difference of the original outputs. For example, if f(x) = 2x and g(x) = x + 1, then (f - g)(x) = 2x - (x + 1) = x - 1. This is not addition or division; it’s subtraction. Reversing the order would give (g - f)(x) = g(x) - f(x), which generally isn’t the same as (f - g)(x).