278 CHAPTER 5 Exponential and Logarithmic Functions Concepts and Vocabulary 4. Given two functions f and g, the , denoted f g, is defined by f g x ( )( ) = . 5. True or False If f x x2 ( ) = and g x x 9, ( ) = + then f g 4 5. ( )( ) = 6. Multiple Choice If f x x 2 ( ) = + and ( ) = g x x 3 , then f g x ( )( ) equals (a) x 3 2 + (b) x 3 2 + (c) x 3 2 + (d) x 3 2 + 7. Multiple Choice If H f g = and H x x 25 4 , 2 ( ) = − which of the following cannot be the component functions f and g? (a) ( ) ( ) = − = f x x g x x 25 ; 4 2 (b) ( ) ( ) = = − f x x g x x ; 25 4 2 (c) ( ) ( ) = − = f x x g x x 25 ; 4 2 (d) ( ) ( ) = − = f x x g x x 25 4 ; 2 8. True or False The domain of the composite function f g x ( )( ) is the same as the domain of g x( ). Skill Building In Problems 9 and 10, evaluate each expression using the values given in the table. 9. x −3 −2 −1 01 2 3 ( ) f x −7 −5 −3 −1 3 5 7 ( ) g x 8 3 0 −1 0 3 8 (a) f g 1 ( )( ) (b) f g 1 ( )( ) − (c) g f 1 ( )( ) − (d) g f 0 ( )( ) (e) g g 2 ( )( ) − (f) f f 1 ( )( ) − 10. x −3 −2 −1 0 1 2 3 ( ) f x 11 9 75 3 1 −1 ( ) g x −8 −3 01 0 −3 −8 (a) f g 1 ( )( ) (b) f g 2 ( )( ) (c) g f 2 ( )( ) (d) g f 3 ( )( ) (e) g g 1 ( )( ) (f) f f 3 ( )( ) 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) g f 1 ( )( ) − (b) g f 0 ( )( ) (c) f g 1 ( )( ) − (d) f g 4 ( )( ) 12. (a) g f 1 ( )( ) (b) g f 5 ( )( ) (c) f g 0 ( )( ) (d) f g 2 ( )( ) In Problems 13–22, for the given functions f and g, find: (a) f g 4 ( )( ) (b) g f 2 ( )( ) (c) f f 1 ( )( ) (d) g g 0 ( )( ) 13. f x x g x x 2 ; 3 1 2 ( ) ( ) = = + 14. f x x g x x 3 2; 2 1 2 ( ) ( ) = + = − 15. ( ) ( ) = − = − f x x g x x 8 3; 3 1 2 2 2 16. f x x g x x 2 ; 1 3 2 2 ( ) ( ) = = − 17. f x x g x x ; 5 ( ) ( ) = = 18. f x x g x x 1; 3 ( ) ( ) = + = 19. f x x g x x ; 1 9 2 ( ) ( ) = = + 20. f x x g x x 2 ; 3 2 2 ( ) ( ) = − = + 21. f x x g x x 3 1 ; 3 ( ) ( ) = + = 22. f x x g x x ; 2 1 3/2 ( ) ( ) = = + In Problems 23–38, for the given functions f and g, find: (a) f g (b) g f (c) f f (d) g g State the domain of each composite function. 23. f x x g x x 2 3; 4 ( ) ( ) = + = 24. f x x g x x ; 2 4 ( ) ( ) = − = − 25. f x x g x x 3 1; 2 ( ) ( ) = − = 26. f x x g x x 1; 4 2 ( ) ( ) = + = + 6 22 x 4 6 8 2 22 (21, 3) (21, 1) (2, 22) (5, 1) (6, 2) (7, 3) (7, 5) (6, 5) (5, 4) (1, 4) (4, 2) (2, 2) (8, 4) (1, 21) (3, 1) y 5 g (x) y 5 f (x) y 4 2
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