- 420 Chapter 6 Exponential And Logarithmic Functions Concepts And Vocabulary 4 Given Two Functions F And G The Denoted 1 (103.58 KiB) Viewed 26 times
420 CHAPTER 6 Exponential and Logarithmic Functions Concepts and Vocabulary 4. Given two functions f and g, the denoted fog, is defined by (fog)(x) = 5. True or False If f(x) = x² and g(x) = √x + 9, then (fog)(4) = 5. 3 6. Multiple Choice If f(x) = √x + 2 and g(x) = then (fog)(x) equals 3 (a) √x + 2 3 Vx (c) 10. X f(x) g(x) X f(x) g(x) +2 -3 -7 -5 8 3 -3 11 -8 -2 - 1 -3 0 12. (a) (gof) (1) (c) (fog)(0) Skill Building In Problems 9 and 10, evaluate each expression using the values given in the table. 9. 21. f(x) = -2 9 -3 -1 7 0 (b) 1 19. f(x) = x; g(x)=x² +9 (d) 0 -1 -1 23. f(x) = 2x + 3; g(x) = 4x 25. f(x) = 3x - 1; g(x)=x² 3 0 5 1 +2 x 3 Vx+2 1 3 0 1 3 0 2 1 -3 2 5 3 (b) (gof)(0) (d) (fog)(4) In Problems 13-22, for the given functions f and g, find: (a) (fog)(4) (b) (gof)(2) (c) (fof) (1) 13. f(x) = 2x; g(x) = 3x² + 1 15. f(x) = 8x² - 3; g(x) = 3 = x² - 17. f(x)=√x; g(x) = 5x (b) (gof) (5) (d) (fog)(2) 3 g(x)=√x x + 1¹ In Problems 23-38, for the given functions f and g. find: (a) fog (b) gof (c) fof (d) gᵒg State the domain of each composite function. 3 7 8 7. Multiple Choice If H = fog and H(x) = V25 - 4x², which of the following cannot be the component functions f and g? 3 -1 -8 (a) f(x) = √25 - x²: g(x) = 4x (b) f(x)=√x g(x) = 25 - 4x² In Problems 11 and 12, evaluate each expression using the graphs of y = f(x) and y = g(x) shown in the figure. 11. (a) (gof) (-1) YA (c) (fog) (-1) 6 (c) f(x) = √25-x; g(x) = 4x² (d) f(x) = √25 - 4x; g(x) = x² 8. True or False The domain of the composite function (fog)(x) is the same as the domain of g(x). (a) (fog)(1) (c) (gof) (-1) (e) (gᵒg) (-2) (a) (fog)(1) (c) (gof) (2) (e) (gᵒg) (1) y = g(x) (-1.3), 2 (-1, 1) -2 4- (d) (gog) (0) -2 (1.4) (2, 2) L 2 (3, 1) (5, 4) (1,-1) 4 (2,-2) (6,5) (7.5) (4,2) (6,2) (5, 1) (b) (fog)(-1) (d) (gᵒf)(0) (1) (ff) (-1) (b) (fog)(2) (d) (gᵒf) (3) (f) (ff) (3) (7,3) 6 - y = f(x) (8,4) 8 X 14. f(x) = 3x + 2; g(x) = 2x² - 1 16. f(x) = 2x²: g(x) = 1 - 3x² 18. f(x) = √x + 1; g(x) = 3x 3 g(x) = x² + 2 20. f(x) = |x-21: 2 22. f(x) = x/2 g(x) = x²1 x + 1 24. f(x)= x; g(x) = 2x - 4 26. f(x) = x + 1; g(x) = x² + 4