444 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 6. If the point 1a, b2 lies on the graph of ƒ, and ƒ has an inverse, then the point lies on the graph of ƒ -1. 7. If ƒ1x2 = x3, then ƒ -11x2 = . 8. If a function ƒ has an inverse, then the graph of ƒ -1 may be obtained by reflecting the graph of ƒ across the line with equation . 9. If a function ƒ has an inverse and ƒ1-32 = 6, then ƒ -1162 = . 10. If ƒ1-42 = 16 and ƒ142 = 16, then ƒ have an inverse because . (does / does not) Determine whether each function graphed or defined is one-to-one. See Examples 1 and 2. 11. x y 0 12. x y 0 13. x y 0 14. x y 0 15. x y 0 16. x y 0 17. y = 2x - 8 18. y = 4x + 20 19. y = 236 - x2 20. y = -2100 - x2 21. y = 2x3 - 1 22. y = 3x3 - 6 23. y = -1 x + 2 24. y = 4 x - 8 25. y = x + 4 x - 3 26. y = x - 8 x + 1 27. y = 21x + 122 - 6 28. y = -31x - 622 + 8 29. y = -2x + 5 30. y = 2x + 3 - 2 31. y = 5 x + 2 32. y = - x - 4 33. y = 23 x + 1 - 3 34. y = -23 x + 2 - 8 Concept Check Answer each question. 35. Can a constant function, such as ƒ1x2 = 3, defined over the set of real numbers, be one-to-one? 36. Can a polynomial function of even degree defined over the set of real numbers have an inverse?
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