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Answer Key 11.1

  1. a
    1. No
    2. Yes
    3. No
    4. Yes
    5. Yes
    6. No
    7. Yes
    8. y2=1+x2
      y=±1+x2
      No
    9. y=2−x
      y=(2−x)2
      Yes
    10. y2=1−x2
      y=±1−x2
      No
  2. All real numbers −∞,∞
  3. a
    5−4x≥0−5−5−4x−4≥−5−4x≤54(−∞,54]
  4. t2≠0
    t≠0 or 0
  5. All real or (−∞,∞)
  6. a
    t2+1≠0−1−1t2≠−1t≠it=R
  7. a
    x−16≥0+16+16x≥16
    [16,∞)
  8. x2−3x−4≠0
    (x−4)(x+1)≠0
    x≠4,1
  9. a
    3x−12≥0+12+123x3≥123x≥4x2−25≠0(x−5)(x+5)≠0x≠5,−5∴x≥4,≠±5
  10. g(0)=4(0)−4
    g(0)=−4
  11. g(2)=−3⋅5−2
    g(2)=−325
  12. f(−9)=(−9)2+4
    f(−9)=81+4
    f(−9)=85
  13. f(10)=10−3
    f(10)=7
  14. f(−2)=3−2−2
    f(−2)=19−2
    f(−2)=19−189
    f(−2)=−179
  15. f(2)=−32−1−3
    f(2)=−31−3
    f(2)=−6
  16. k(2)=−2⋅42(2)−2
    k(2)=−2⋅44−2
    k(2)=−2⋅42
    k(2)=−32
  17. p(−2)=−2⋅42(−2)+1+1
    p(−2)=−2⋅4−4+1+1
    p(−2)=−2⋅4−3+1
    p(−2)=−264+1
    p(−2)=−132+1⇒−3132
  18. h(−4x)=(−4x)3+2
    h(−4x)=−64x3+2
  19. h(n+2)=4(n+2)+2
    h(n+2)=4n+8+2
    h(n+2)=4n+10
  20. h(−1+x)=3(−1+x)+2
    h(−1+x)=−3+3x+2
    h(−1+x)=3x−1
  21. h(13)=−3⋅213+3
    h(13)=−23⋅323
    h(13)=−8⋅323
    h(13)=−2423
  22. h(x4)=(x4)2+1
    h(x4)=x8+1
  23. h(t2)=(t2)2+t
    h(t2)=t4+t
  24. f(0)=|3(0)+1|+1
    f(0)=1+1 or 2
  25. f(−6)=−2|−(−6)−2|+1
    f(−6)=−2|6−2|+1
    f(−6)=−2(4)+1
    f(−6)=−8+1 or −7
  26. f(10)=|10+3|
    f(10)=13
  27. p(5)=−|5|+1
    p(−5)=−5+1
    p(−5)=−4

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