1. MAT150 Class #3 Find sums, differences, products, and quotients of two functions Form average cost functions Find the composition of two functions

2. SUM, DIFFERENCE, PRODUCT, AND QUOTIENT OF FUNCTIONS

3. (iv)Quotient (i)Sum (ii)Difference (iii)Product

4. EXAMPLE Combining Functions Let Find each of the following functions and give their domains if applicable.

5. 5 Copyright © 2015, 2011, and 2009 Pearson Education, Inc. EXAMPLE continued Solution

6. 6 Copyright © 2015, 2011, and 2009 Pearson Education, Inc. EXAMPLE continued

7. EXAMPLE continued

8. COMPOSITION OF FUNCTIONS If f and g are two functions, the composition of function f with function g is written as and is defined by the equation where the domain of values x in the domain of g for which g(x) is in the domain of f. consists of those

9. COMPOSITION OF FUNCTIONS

10. EXAMPLE combined Let Find each of the following.

11. EXAMPLE continued

12. EXAMPLE Finding Composite Functions Let Find each composite function and give the domain of each new function formed

13. EXAMPLE continued

14. EXAMPLE Finding the Domain of a Composite Function Solution Step 1 Let A be the domain of the inner function g. We may find A by first finding the values of x for which g is not defined.

15. EXAMPLE continued Step 2 Let B be the set of values of x for which g(x) is in the domain of f. As before, we may do this by finding the values of x for which g(x) is not in the domain of f.

16. EXAMPLE The demand for a certain electronic component is given by p(x) = 1000 – 2x. Producing and selling x components involves a monthly fixed cost of $1999 and a production cost of $4 for each component. a.Write the equations that model total revenue and total cost as functions of the components produced and sold in a month. b.Write the equation that models the profit as a function of the components produced and sold during a month. c.Find the maximum possible monthly profit.

17. EXAMPLE continued a.Write the equations that model total revenue and total cost as functions of the components produced and sold in a month.

18. EXAMPLE b. Write the equation that models the profit as a function of the components produced and sold during a month.

19. EXAMPLE c. Find the maximum possible monthly profit.

20. EXAMPLE Oil is spilled from a tanker into the Pacific Ocean and the area of the oil spill is a perfect circle. The radius of this oil slick increases at the rate of 2 miles per hour. a.Express the area of the oil slick as a function of time. b.Calculate the area covered by the oil slick in six hours.

21. EXAMPLE continued Solution The area of the oil slick is a function its radius. The radius is a function time: increasing 2 mph a. The area is a composite function

22. EXAMPLE continued Solution b. Substitute t =.