## Algebra and Trigonometry 10th Edition

The notation (f - g)(1) can be rewritten as f(1) - g(1). Solving by subtracting the functions then evaluating at 1 will yield the same result as evaluating each function and then subtracting. In this question: f(x) = x + 3 g(x) = $x^{2}$ - 2 Method 1: Subtract the functions then evaluate First we want to subtract the two functions. The new function will be called h(x). h(x) = f(x) - g(x) h(x) = (x + 3) - ($x^{2}$ - 2) h(x) = x + 3 - $x^{2}$ + 2 Combine like variables to get: h(x) = -$x^{2}$ + x + 5 Evaluate at x = 1: h(1) = -$(1)^{2}$ + 1 + 5 = 5 Method 2: Evaluate the functions and then subtract First we want to evaluate f(x) at x = 1: f(1) = 1 + 3 = 4 Then we want to evaluate g(x) at x = 1: g(1) = $(1)^{2}$ - 2 = -1 Subtract the numbers together: (f - g)(1) = 4 - (-1) = 5 Using both methods (f - g)(1) = 5