{ EXAMPLE 1 The functions defined by the formulas { f(x) = √x and have domains D(f) = [0, ∞) and D(g) = (-∞0, 1]. The points common to these do- mains are the points [0, ∞) n(-∞, 1] = [0, 1]. The following table summarizes the formulas and domains for the various algebraic com- binations of the two functions. We also write f g for the product function fg. Function ƒ + g f-g g - f f.g f/g g/f Formula (f + g)(x) = √x + VI-x (f - g)(x) = √x - VT-x (8 - f)(x) = V1 -x - √x (f.g)(x) = f(x)g(x) = √x(1-x) f(x) //(x) tla R = g(x) = VT-x g(x) g(x) f(x) = HEL Domain [0, 1] = D(f) D(g) [0, 1] [0, 1] [0, 1] [0, 1) (x = 1 excluded) (0, 1] (x = 0 excluded) The graph of the function f + g is obtained from the graphs off and g by adding the corresponding y-coordinates f(x) and g(x) at each point x = D(f) nD(g), as in Figure 1.25. The graphs of f + g and f g from Example 1 are shown in Figure 1.26.