f(x) = 2 – 3x g(x) = –2x2 + 3x – 1 h(x) =

Exercise. A. Simplify the following expressions with the given functions.

Notation and Algebra of Functions

2x – 1x – 2

1. f(2) + f(3)

5. f(0) + g(0) + h(0)

2. 2f(3) 4. [h(2)]23. 2g(0) + g(1)

10. [f(3)]2 – [g(3)]2

6. 3h(1) – g(–2 )

8. f(2)/3 + f(3)/2

11. f(0) + g(0) + h(0)

9. 2f(–3) – 2g(–1)

14. [h(1/2)]2

17. g(f(0))

12. [f(3) – g(3)]2

13. h(1) / h(–1 )

7. 3h(1) – g(–2 )

15. [f(1/2)]216. [g(1/2)]2

18. f(g(0)) 19. g(h(0))

20. h(g(0)) 21. f(h(0)) 22. h(f(0))

f(x) = 3 + 2x g(x) = –x2 + 3x – 2 h(x) =

Exercise. B. Simplify the following expressionswith the given functions.

Notation and Algebra of Functions

x – 1x – 2

23. f(2a)

27. 2h(a)

24. g(2a) 26. h(2a) 25. 2g(a)

28. f(3 + b) 29. g(3 + b) 30. h(3 + b)

31. f(3 + b) – f(b) 32. g(3 + b) – g(b) 33. h(3 + b) – h(b)

34. f(3 + b) – f(3 – b) 35. g(3 + b) – g(3 – b)

36. g(x) + 3f(x) 37. 2g(x) + [f(x)]2 38. g(x) / h(x)

c. Let x = the number of boxes in one order. We have coupons for $7 off for one order of x boxes of peanuts. What is the cost P(x) for x boxes peanuts with the coupon?

39. a. Peanuts cost $9.00/box, what is the cost of x boxes of peanuts? b. Cashews cost $12.00/box, what is the cost of x boxes of cashews?

Notation and Algebra of Functionsc. Let x = the number of boxes in one order. There is a surcharge (special tax) of $5 per cashew–order for x boxes of cashews. What is the cost C(x) for an order of x boxes cashews?

d. Let x = the number of boxes in one order.Simply 2P(x) + 3C(x). What does this function represent?

40. Recall that the area of a circle is A = π * r2. A circle city of radius r = 5 km is expanding outwardly with the radius of the city increasing at a rate of 2 km every year. Let x = the number of years, a. what is the radius r(x) of the city after x years? b. after 10 years, what is r(10)? what is the area when x = 10? c. what is the area A(x) of the city after x years? d. what is A(6)? A(8)? A(8) – A(6)? What does each expression mean?

r=5 kmexpanding (2 km/yr)