7.1 Review Worksheet (continued)
7.1.2 Inverses of Relations and Functions Graph the relation and connect the points. Then graph the inverse. Identify the domain and range of each relation. 6. 7.
x y
− 4 − 2
− 2 0 2 4 − 1 0 1 2
x y
− 1 2 3 5 1 3 5 5
Use inverse operations to write the inverse of each function. 8. f ( x ) = 0.825 x 9. f ( x ) = − f x x ( ) 1
3 4
x
10. f ( x ) ( )
= f x
0.25
= + f x x ( ) 1 5
11. f ( x ) = 21 − 32 x
12. f ( x ) = 145 + 12.5 x
13. f ( x )
12
Graph each function. Then write and graph its inverse. 14. f ( x ) 15. f ( x ) ( 15) = − f x x ( ) 2
= − f x x ( ) 4 5
16. f ( x ) = 1.21 x
3
17. A linear model projects that the number of bachelor’s degrees awarded in the United States will increase by 19,500 each year. In 2001, 1.28 million bachelor’s degrees were awarded. Use the inverse function to predict the number of years after 2001 that 1.7 million bachelor’s degrees will be awarded. Source: nces.ed.gov
7.1.3 Logarithmic Functions Write each exponential equation in logarithmic form. 18. x 2.5 = 32 19. 6 x = 216
20. 1.2 0 = 1
21. 4 − 1 = 0.25
119
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