290 CHAPTER 5 Exponential and Logarithmic Functions ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 5.2 Assess Your Understanding 1. Suppose ( ) = − f x x4 2. Find ( ) + f x 2 4 (pp. 65–67) 2. Where is the function ( ) = f x x2 increasing? Where is it decreasing? (pp. 89–90) 3. What is the domain of ( ) = + + − f x x x x 5 3 18 ? 2 (pp. 236–237) 4. Simplify: + − x x 1 1 1 1 2 (pp. A35–A42) 5. If x1 and x2 are any two different inputs of a function f, then f is one-to-one if . 6. If every horizontal line intersects the graph of a function f at no more than one point, then f is a(n) function. 7. If f is a one-to-one function and ( ) = f 3 8, then ( ) = −f 8 1 . 8. If −f 1 is the inverse of a function f, then the graphs of f and −f 1 are symmetric with respect to the line . 9. If the domain of a one-to-one function f is [ )∞ 4, , then the range of its inverse function −f 1 is. 10. True or False If f and g are inverse functions, then the domain of f is the same as the range of g . 11. Multiple Choice If ( ) −2, 3 is a point on the graph of a oneto-one function f, which of the following points is on the graph of −f ?1 (a) ( ) − 3, 2 (b) ( ) − 2, 3 (c) ( ) −3, 2 (d) ( ) − − 2, 3 12. Multiple Choice Suppose f is a one-to-one function with a domain of { } ≠ x x 3 and a range of { } ≠ y y 2 3 . Which of the following is the domain of −f ?1 (a) { } ≠ x x 3 (b) All real numbers (c) { } ≠ ≠ x x x 2 3 , 3 (d) { } ≠ x x 2 3 Concepts and Vocabulary Skill Building In Problems 13–20, determine whether the function is one-to-one. 13. 20 Hours Domain 25 Hours 30 Hours 40 Hours $500 $625 $750 $1000 Range 14. Bob Domain Dave John Lamonte Karla Debra Dawn Shanice Range 15. 20 Hours Domain 25 Hours 30 Hours 40 Hours $625 $750 $1000 Range 16. Bob Domain Dave John Lamonte Karla Debra Shanice Range 17. ( ) ( ) ( ) ( ) { } − 2, 6 , 3, 6 , 4, 9 , 1, 10 18. ( ) ( ) ( ) ( ) { } − − 2, 5 , 1, 3 , 3, 7 , 4, 12 19. ( ) ( ) ( ) ( ) { } 0, 0 , 1, 1 , 2, 16 , 3, 81 20. ( ) ( ) ( ) ( ) { } 1, 2 , 2, 8 , 3, 18 , 4, 32 In Problems 21–26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. 21. x y 3 3 23 23 22. x y 3 3 23 23 23. x y 3 3 23 23 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
RkJQdWJsaXNoZXIy NjM5ODQ=