- 420 Chapter 6 Exponential And Logarithmic Functions Concepts And Vocabulary 4 Given Two Functions F And G The Denoted 1 (104.41 KiB) Viewed 32 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 X 3 (a) Vx+ 2 3 Vx (c) 10. X f(x) g(x) X f(x) g(x) +2 Skill Building In Problems 9 and 10, evaluate each expression using the values given in the table. 9. -3 -7 8 -2 -1 -5 -3 3 0 -3 -2 11 9 -8 -3 12. (a) (gof) (1) (c) (fog)(0) 21. f(x) = -1 7 0 19. f(x)= x; g(x) = 1 x² +9 3 =x+1² 8(x)=√x 3 (b) +2 Vx (d) 0 23. f(x) = 2x + 3; g(x) = 4x 25. f(x) = 3x - 1; g(x) = x² -1 -1 3 √x + 2 0 5 1 1 3 0 1 3 0 2 1 -3 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 - 1 / x² 17. f(x)=√x: g(x) = 5x 2 5 3 (b) (gof) (0) (d) (fog) (4) (b) (gof) (5) (d) (fog)(2) 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 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- 8 7. Multiple Choice If H = fog and H(x) = V25 - 4x², which of the following cannot be the component functions fand g? 3 -1 -8 (a) f(x) = √25 x²: g(x) = 4x (b) f(x)=√x: g(x) = 25 - 4x² (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 (d) (gog) (0) 4(1.4) -2 (2, 2) 2 (5, 4) (1,-1) (3.1) (4.2) 16.2) (5, 1) ✓ 4 (2,-2) (6,5) (7.5) .. L (7,3) (b) (fog) (-1) (d) (gof) (0) (f) (ff) (-1) 6 y = f(x) (b) (fog)(2) (d) (gᵒf) (3) (f) (ff) (3) 16. f(x) = 2x²: g(x) = 1 - 3x² 18. f(x) = √x + 1; 20. f(x) = |x-2: (8,4) 8 X 2 22. f(x) = x³/2; g(x)=; x + 1 14. f(x) = 3x + 2; g(x) = 2x² - 1 g(x) = 3x 3 g(x) = x² + 2 24. f(x)=x; g(x) = 2x - 4 26. f(x) = x + 1; g(x) = x² + 4