Combinations and Decomposition of Functions

Notes

Lesson 1.6 Combinations of Functions Objectives: • Add, subtract, multiply and divide functions. • Find the composition of one function with another function. • Decompose composite functions. Add, subtract, multiply and divide function. 1. Let f and g be two functions with overlapping domains. Then, for all x common to both domains, the sum, difference, product, and quotient of f and g are defined as follows. a. Sum: (f + g)(x) = f(x) + g(x) b. Difference: (f – g)(x) = f(x) – g(x) c. Product: (fg)(x) = f(x) · g(x) d. Quotient:      f g =f(x) g(x) , g(x) ≠ 0 Example 1: If f(x) = -2x + 5, g(x) = -3x2 – 1 and h(x) =x - 1 , find the following combinations of function. a. (f + g)(x) = b. (f – h)(x) = c. (fg)(x) = d.      g h (x) = Example 2: If f(x) = 2x2 – 3 and g(x) = 8x – 10, evaluate each combination of functions. a. (f + g)(-1) = b. (f – g)(-2) = c. (fg)(7) = d. (f g )(3) = 2. For functions f and g, the domain of the combination of functions of f + g, f – g, and fg, is the intersection of the individual domains of f(x) and g(x). The intersection of the individual domains of f(x) and g(x) are all the x values that are in both domains of f(x) and g(x). The domain of the c...