Subtraction of Functions

To subtract two functions, subtract their outputs. For example, if f (x) = 2x - 1 and g(x) = x + 4, then (f - g)(2) = f (2) - g(2) = 3 - 6 = - 3. (f - g)(x) = f (x) - g(x) = (2x - 1) - (x + 4) = x - 5. Here is a graph of y = f (x), y = g(x), and y = (f + g)(x):

Subtraction of Functions

The y-coordinate of each point on the graph of y = (f - g)(x) is the result of subtracting the y-coordinate of g(x) from the y-coordinate of f (x). For example, as noted above, f (2) = 3, g(2) = 6, and (f - g)(2) = 3 - 6 = - 3.