9 4 Operations with Functions 9 4 LEARNING

9 -4 Operations with Functions 9 -4 LEARNING GOALS 9. 4. 1 Add, subtract, multiply, and divide functions. 9. 4. 2 Write and evaluate composite functions. 9. 4. 3 Write composite functions and determine restrictions on their domain. Addition Subtraction Multiplication Division Example 1: Adding and Subtracting Functions Given f(x) = 4 x 2 + 3 x – 1 and g(x) = 6 x + 2, find each function. A. ADD. (f + g)(x) B. SUBTRACT. (f – g)(x) When you divide functions, be sure to note any domain restrictions. Example 2: Multiplying and Dividing Functions Given f(x) = 6 x 2 – x – 12 and g(x) = 2 x – 3, find each function. A. MULTIPLY. (fg)(x) B. DIVIDE.

9 -4 Operations with Functions Given f(x) = 5 x – 6 and g(x) = x 2 – 5 x + 6, find each function. C. SUBTRACT. (f – g)(x) Given f(x) = x + 2 and g(x) = x 2 – 4, find each function. D. DIVIDE. Another function operation uses the output from one function as the input for a second function. This operation is called the ___________. Reading Math The composition (f o g)(x) or f(g(x)) is read “f of g of x. ” Caution! Be careful not to confuse the notation for multiplication of functions with composition fg(x) ≠ f(g(x))

9 -4 Operations with Functions Use order of operations for these expressions. To find f(g(3)), evaluate g(3) first and then substitute the result into f. Example 3: Evaluating Composite Functions Given f(x) = 2 x and g(x) = 7 – x, find each value. A. f(g(4)) Step 1 Find g(4) Step 2 Find f(_____) Given f(x) = 2 x – 3 and g(x) = x 2, find each value. B. g(f(3)) Step 1 Find f(3) Step 2 Find g(_____) The domain of a composite function depends on the “inner” function and the “outer” function. Example 4: Writing Composite Functions Given f(x) = x 2 – 1 and g(x) = the domain of each. , write each composite function. State A. f(g(x)) The domain of f(g(x)) is {x _______} because g(___) is undefined.

9 -4 Operations with Functions Given f(x) = 3 x – 4 and g(x) = + 2 , write each composite. State the domain of each. B. g(f(x)) DOMAIN: C. f(g(x)) DOMAIN: Example 5: Business Application Jake imports furniture from Mexico. The exchange rate is 11. 30 pesos per U. S. dollar. The cost of each piece of furniture is given in pesos. The total cost of each piece of furniture includes a 15% service charge. A. Write a composite function to represent the total cost of a piece of furniture in dollars if the cost of the item is c pesos. Step 1 Write a function for the total cost in U. S. dollars. Step 2 Write a function for the cost in dollars based on the cost in pesos. Step 3 Find the composition D(P(c)). B. Find the total cost of a table in dollars if it costs 1800 pesos.