section3_6 - Section 3.6 Sum Difference Product Quotient...

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Unformatted text preview: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 1 of 14 Example 1: For the functions f ( x) = 2 x 2 − 4 x + 1 and g ( x) = 7 x, find f + g , f − g , fg , and their domains. Solution to Example 1: f , g Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 2 of 14 Example 2: For the functions f ( x) = 3 x + 1 and g ( x) = 4 x + 5, find ( f + g ) (1), ( f − g ) (2), f (−2), and ( f g ) (3). g Solution to Example 2: ( fg ) (−1), Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 3 of 14 Example 3: For the functions f ( x) = x 2 − 5 and g ( x) = x3 + 1, find f g , g f , and their domains. Solution to Example 3: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 4 of 14 Example 4: Solution to Example 4: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 5 of 14 Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 6 of 14 Example 5: Solution to Example 5: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 7 of 14 Example 6: Solution to Example 6: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 8 of 14 Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 9 of 14 Example 7: Solution to Example 7: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 10 of 14 Example 8: Solution to Example 8: Section 3.6 Sum, Difference, Product, Quotient, and Composition of Functions Page 11 of 14 Exercise Set 3.6: Combining Functions Answer the following. 1. f 8 6 4 2 −6 −4 −2 2 4 6 x 8 y For each of the following problems: (a) Find f + g and its domain. g (b) Find f − g and its domain. (c) Find fg and its domain. (d) Find f and its domain. g Note for (a)-(d): Do not sketch any graphs. 3. 4. 5. f ( x ) = 2 x + 3; g ( x ) = x 2 − 4 x − 12 f ( x ) = 2 x3 − 5 x; g ( x) = x 2 + 8 x + 15 −2 −4 −6 (a) Find f (−3) + g (−3) . (b) Find f (0) + g (0) . (c) Find f (−6) + g (−6) . (d) Find f (5) + g (5) . (e) Find f (7) + g (7) . (f) Sketch the graph of f + g . (Hint: For any x value, add the y values of f and g.) (g) What is the domain of f + g ? Explain how you obtained your answer. 2. f y f ( x) = 3 x ; g ( x) = x+2 x −1 2x 4 ; g ( x) = x−5 x−5 6. 7. 8. 9. f ( x) = f ( x ) = x − 6 ; g ( x ) = 10 − x f ( x) = 2 x − 3 ; g ( x) = x + 4 f ( x) = x 2 − 9 ; g ( x) = x 2 + 4 8 6 4 2 −6 −4 −2 10. f ( x) = 49 − x 2 ; g ( x) = x − 3 g Find the domain of each of the following functions. x 2 4 6 8 11. f ( x) = 2 + x −1 x −3 3 x −2 −4 −6 12. h( x) = x + 2 − (a) Find f (−2) − g (−2) . (b) Find f (0) − g (0) . (c) Find f (−4) − g (−4) . (d) Find f (2) − g (2) . (e) Find f (4) − g (4) . (f) Sketch the graph of f − g . (Hint: For any x value, subtract the y values of f and g.) (g) What is the domain of f − g ? Explain how you obtained your answer. 13. g ( x) = 3 x +1 − x−7 x−2 5 x−2 + +7 x + 6 x −1 14. f ( x) = 15. f ( x) = x+2 x −5 x−3 x −1 16. g ( x) = Exercise Set 3.6: Combining Functions Answer the following, using the graph below. 8 y For each of the following problems: (a) Find f g and its domain. (b) Find g f and its domain. 33. f ( x) = x 2 + 3x; g ( x) = 2 x − 7 f 6 4 2 g x 2 4 6 8 34. f ( x) = 6 x + 2; g ( x) = 7 − x 2 35. f ( x) = x 2 ; g ( x) = 3 x+5 1 x−4 −6 −4 −2 −2 −4 −6 17. (a) g (2) (c) f ( 2) 18. (a) g (0) (c) f (0) 19. (a) 20. (a) 21. (a) 22. (a) 23. (a) 24. (a) (b) f (g (2)) (d) g ( f (2)) (b) f (g (0)) (d) g ( f (0)) (b) (b) (b) (b) (b) (b) 36. f ( x) = ; g ( x) = x 2 37. f ( x) = x + 7 ; g ( x) = −5 − x 38. f ( x) = 3 − x ; g ( x) = 9 − 2 x (f (f g )(− 3) g )(− 1) f )(3) f )(5) g )(4 ) g )(− 5) (g (g f )(− 3) f )(− 1) g )(− 2 ) g )(− 3) f )(4 ) g )(2 ) Answer the following. 39. Given the functions f ( x) = x 2 + 2 and g ( x) = 5 x − 8 , find: (a) (c) (e) (g) f (g (1)) f (g (x )) f ( f (1)) f ( f (x )) (f (f (f (g (g (g (f (f (b) (d) (f) (h) g ( f (1)) g ( f (x )) g (g (1)) g (g (x )) Use the functions f and g given below to evaluate the following expressions: f ( x) = 3 − 2 x and g ( x) = x 2 − 5 x + 4 40. Given the functions f ( x) = x + 1 and g ( x) = 3 x − 2 x 2 , find: 25. (a) g (0) (c) f (0) 26. (a) g (−1) (c) f (−1) 27. (a) 28. (a) 29. (a) 30. (a) 31. (a) 32. (a) (b) f (g (0)) (d) g ( f (0)) (b) f (g (− 1)) (d) g ( f (− 1)) (b) (b) (b) (b) (b) (b) (a) (c) (e) (g) f (g (− 3)) f (g (x )) f ( f (− 3)) f ( f (x )) (b) (d) (f) (h) g ( f (− 3)) g ( f (x )) g (g (− 3)) g (g (x )) x +1 and x−2 41. Given the functions f ( x) = g ( x) = 3 , find: x−5 (f g )(− 2) g )(4 ) f )(6) f )(− 4 ) g )(x ) f )(x ) (g f )(− 2) f )(4 ) g )(6) g )(− 4 ) f )(x ) g )(x ) (f (f (f (f (f (g (g (g (g (g (a) f (g (− 2)) (c) f (g (x )) (b) g ( f (− 2)) (d) g ( f (x )) 2x and x+5 42. Given the functions f ( x) = g ( x) = 7−x , find: x −1 (a) f (g (3)) (c) f (g (x )) (b) g ( f (3)) (d) g ( f (x )) Exercise Set 3.6: Combining Functions 43. Given the functions f ( x ) = x 2 − 1, g ( x) = 3x − 5, and h( x) = 1 − 2 x, find: (a) f (g (h(2))) (c) f g h 44. Given the functions (b) g (h( f (3))) (d) g h f f ( x) = 2 x 2 + 3, g ( x) = x + 4, and h( x) = 3 x − 2, find: (a) f (g (h(1))) (c) f g h 45. Given the functions (b) g (h( f (1))) (d) g h f f ( x ) = x 2 + 4, g ( x) = x + 3 , and h( x ) = 2 x + 1, find: (a) h( f (g (4))) (c) f g h 46. Given the functions f ( x) = 1 x2 (b) f (g (h(0))) (d) h f g , g ( x) = x − 2 , and h( x) = 3 − 4 x, find: (a) h( f (g (5))) (c) f g h (b) f (g (h(− 2))) (d) h f g ...
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This document was uploaded on 07/14/2010.

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