61. Which, if any, are parallel? 62. Which, if any, are perpendicular? > Synthesis 63. Let p(a) represent the number of pounds of grass seed required to seed a lawn with area a. Let c(s) represent the cost of s pounds of grass seed. Which composition makes sense: (cop) (a) or (poc) (s) ? What does it represent? 64. Write equations of two functions f and g such that fog = gof = x. (In Section 5.1, we will study in- verse functions. If fog = gof = x, functions f and g are inverses of each other.) Mid-Chapter Mixed Review termine whether the statement is true or false. f(c) is a relative maximum if (c, f( c) ) is the highest 2. If f and g are functions, then the domain of the func- point in some open interval containing c. [2.1] tions f + g, f - g, fg, and f/ g is the intersection of the domain of f and the domain of g. [2.2] In general, (fog) (x) # (8. f) (x), [2.3]122 CHAPTER 2 More on Functions 5. Using the graph, determine any relative maxima 4. Determine the intervals on which the function is minima of the function and the intervals on which (a) increasing; (b) decreasing; (c) constant. [2.1] function is increasing or decreasing. [2.1] (-1.29, 6.30) 6 -5-4-3 2 1 1 - 3 (1.29, -2.30) 7. Window Design. Lucas is designing a window for 6. Determine the domain and the range of the function peak of an A-frame house. The base is 4 ft more the graphed in Exercise 4. [2.1] the height h. Express the area of the window as a f tion of the height. [2.1] 9. Graph the function defined as 8. For the function defined as Jx+ 2, forx 0, find f(-5), f(-3), f( -1), and f(6). [2.1] Given that f(x) = 3x - 1 and g(x) = x2 + 4, find each of the following, if it exists. [2.2] 10 . ( f + 8 ) ( - 1 ) 2 11. (f8) (0) 12. (8 - f) (3 ) 13 . (8 /f ) ( 3 ) For each pair of functions in Exercises 14 and 15: a) Find the domains of f, 8, f + 8,f - 8,fg, ff,f/g, and g /f. b) Find ( f + 8 ) ( x ), ( f - 8 ) ( x), (f8 ) ( x ), ( ff) ( x ), (f/8 ) ( x), and (8/f) (x). [2.2] 14. f ( x ) = 2x + 5, 8(x) = -x-4 15. f ( x ) = x - 1, 8(x) = Vx+ 2 For each function fin Exercises 16 and 17, construct and simplify the difference quotient f ( x + h ) - f (x ) [2.2] h 16. f(x ) = 4x - 3 17. f(x ) = 6 - x2 18. ( fog ) ( 1 ) Given that f( x) = 5x - 4, 8(x) = x3 + 1, and h(x) = x2 - 2x + 3, find each of the following. [2.3] 20 . (fo f ) (0 ) 19. (8 oh) (2 ) 21. ( hof ) (-1 ) Find (fog) (x) and (g . f) (x) and the domain of each. [2.3] 22. f ( x ) = 2x, 8 (x) = 6x + 4 23. f ( x) = 3x + 2, 8(x) = Vx