College Algebra, 2013a

222 Linear and Quadratic Functions
2.4.2 Answers
1. [ 1
3 , 3] 2. ( −∞, − 12 ) (
7 ∪ 8
7 , ∞)
3. (−3, 2) 4. (−∞, 1] ∪ [3, ∞)
5. No solution 6. (−∞, ∞)
7. (−3, 2] ∪ [6, 11) 8. [3, 4) ∪ (5, 6]
9. [ − 12
7 , − 6 ]
5
10. (−∞, −4) ∪ ( 2
3 , ∞)
11. ( −∞, − 4 3]
∪ [6, ∞) 12. (−∞, −5)
13. No Solution. 14. [ −7, 5 ]
3
15. ( 1, 5 )
3
16. (−∞, ∞)
17. (−∞, −3] ∪ [1, ∞) 18. ( −∞, − 1 4)
∪
(
−
1
4 , ∞)
19. No solution 20. (−∞, ∞)
21. {2} 22. No solution
23. [ − 1 3 , 4] 24. (0, 1)
(
√ ) ( √ )
(
25. −∞, 1 − 6
2
∪ 1+ 6
2 , ∞ 26.
27. ( −3 √ 2, − √ ] [
11 ∪ − √ ) (
7, 0 ∪ 0, √ ] [ √11, √ )
7 ∪ 3 2
−∞, 5−√ 73
6
] [ √ )
∪ 5+ 73
6
, ∞
28. [ −2 − √ 7, −2+ √ 7 ] ∪ [1, 3]
29. (−∞, ∞) 30. (−∞, −1] ∪{0}∪[1, ∞)
31. [−6, −3] ∪ [−2, ∞)
( )
32. (−∞, 1) ∪
2, 3+√ 17
2
33. P (x) ≥ 50 on [10, 15]. This means anywhere between 10 and 15 bottles of tonic need to be
sold to earn at least $50 in profit.
34. C(x) ≤ 11 on [2, 8]. This means anywhere between 2000 and 8000 pens can be produced and
the cost will not exceed $1100.
35. T (t) > 42 on (8 − 2 √ 11, 8+2 √ 11) ≈ (1.37, 14.63), which corresponds to between 7:22 AM
(1.37 hours after 6 AM) to 8:38 PM (14.63 hours after 6 AM.) However, since the model is
valid only for t, 0≤ t ≤ 12, we restrict our answer and find it is warmer than 42 ◦ Fahrenheit
from 7:22 AM to 6 PM.