Algebra and Trigonometry 10th Edition

(f - g)(3t) = -9$t^{2}$ + 3t + 5
The notation (f - g)(3t) can be rewritten as f(3t) - g(3t). Solving by subtracting the functions then evaluating at 3t 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 = 3t: h(3t) = -$(3t)^{2}$ + 3t + 5 = -9$t^{2}$ + 3t + 5 Method 2: Evaluate the functions and then subtract First we want to evaluate f(x) at x = 3t: f(3t) = 3t + 3 Then we want to evaluate g(x) at x = 3t: g(3t) = $(3t)^{2}$ - 2 = 9$t^{2}$ - 2 Subtract the numbers together: (f - g)(3t) = 3t + 3 - (9$t^{2}$ - 2) = 3t + 3 - 9$t^{2}$ + 2 = -9$t^{2}$ + 3t + 5 Using both methods (f - g)(3t) = -9$t^{2}$ + 3t + 5