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Answer Key 11.1

  1. [latex]\phantom{a}[/latex]
    1. No
    2. Yes
    3. No
    4. Yes
    5. Yes
    6. No
    7. Yes
    8. [latex]y^2=1+x^2[/latex]
      [latex]y=\pm \sqrt{1+x^2}[/latex]
      No
    9. [latex]\sqrt{y}=2-x[/latex]
      [latex]y=(2-x)^2[/latex]
      Yes
    10. [latex]y^2=1-x^2[/latex]
      [latex]y=\pm \sqrt{1-x^2}[/latex]
      No
  2. All real numbers [latex]-\infty, \infty[/latex]
  3. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} 5&-&4x&\ge &0 \\ -5&&&&-5 \\ \hline &&\dfrac{-4x}{-4}&\ge &\dfrac{-5}{-4} \\ \\ &&x&\le &\dfrac{5}{4} \\ \end{array}[/latex][latex]\left(-\infty, \dfrac{5}{4}\right][/latex]
  4. [latex]t^2\neq 0[/latex]
    [latex]t\neq \sqrt{0}\text{ or }0[/latex]
  5. All real or [latex](-\infty, \infty)[/latex]
  6. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} t^2&+&1&\neq &0 \\ &-&1&&-1 \\ \hline &&t^2&\neq &-1 \\ &&t&\neq & i \\ \\ &&t&=&\mathbb{R} \end{array}[/latex]
  7. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{rrrrr} x&-&16&\ge &0 \\ &+&16&&+16 \\ \hline &&x&\ge &16 \\ \end{array}[/latex]
    [latex][16, \infty)[/latex]
  8. [latex]x^2-3x-4\neq 0[/latex]
    [latex](x-4)(x+1)\neq 0[/latex]
    [latex]x\neq 4,1[/latex]
  9. [latex]\phantom{a}[/latex]
    [latex]\begin{array}[t]{ll} \begin{array}[t]{rrrrr} 3x&-&12&\ge &0 \\ &+&12&&+12 \\ \hline &&\dfrac{3x}{3}&\ge &\dfrac{12}{3} \\ \\ &&x&\ge &4 \end{array} &\hspace{0.25in} \begin{array}[t]{rrl} x^2-25&\neq &0 \\ (x-5)(x+5)&\neq &0 \\ x&\neq &5, -5 \\ \\ \therefore x&\ge &4, \neq \pm 5 \end{array} \end{array}[/latex]
  10. [latex]g(0)=\cancel{4(0)}-4[/latex]
    [latex]\phantom{g(0)}=-4[/latex]
  11. [latex]g(2)=-3\cdot 5^{-2}[/latex]
    [latex]\phantom{g(2)}=-\dfrac{3}{25}[/latex]
  12. [latex]f(-9)=(-9)^2+4[/latex]
    [latex]\phantom{f(-9)}=81+4[/latex]
    [latex]\phantom{f(-9)}=85[/latex]
  13. [latex]f(10)=10-3[/latex]
    [latex]\phantom{f(10)}=7[/latex]
  14. [latex]f(-2)=3^{-2}-2[/latex]
    [latex]\phantom{f(-2)}=\dfrac{1}{9}-2[/latex]
    [latex]\phantom{f(-2)}=\dfrac{1}{9}-\dfrac{18}{9}[/latex]
    [latex]\phantom{f(-2)}=-\dfrac{17}{9}[/latex]
  15. [latex]f(2)=-3^{2-1}-3[/latex]
    [latex]\phantom{f(2)}=-3^1-3[/latex]
    [latex]\phantom{f(2)}=-6[/latex]
  16. [latex]k(2)=-2\cdot 4^{2(2)-2}[/latex]
    [latex]\phantom{k(2)}=-2\cdot 4^{4-2}[/latex]
    [latex]\phantom{k(2)}=-2\cdot 4^2[/latex]
    [latex]\phantom{k(2)}=-32[/latex]
  17. [latex]p(-2)=-2\cdot 4^{2(-2)+1}+1[/latex]
    [latex]\phantom{p(-2)}=-2\cdot 4^{-4+1}+1[/latex]
    [latex]\phantom{p(-2)}=-2\cdot 4^{-3}+1[/latex]
    [latex]\phantom{p(-2)}=-\dfrac{2}{64}+1[/latex]
    [latex]\phantom{p(-2)}=-\dfrac{1}{32}+1 \Rightarrow \dfrac{-31}{32}[/latex]
  18. [latex]h(-4x)=(-4x)^3+2[/latex]
    [latex]\phantom{h(-4x)}=-64x^3+2[/latex]
  19. [latex]h(n+2)=4(n+2)+2[/latex]
    [latex]\phantom{h(n+2)}=4n+8+2[/latex]
    [latex]\phantom{h(n+2)}=4n+10[/latex]
  20. [latex]h(-1+x)=3(-1+x)+2[/latex]
    [latex]\phantom{h(-1+x)}=-3+3x+2[/latex]
    [latex]\phantom{h(-1+x)}=3x-1[/latex]
  21. [latex]h(\dfrac{1}{3})=-3\cdot 2^{\frac{1}{3}+3}[/latex]
    [latex]\phantom{h(\dfrac{1}{3})}= -2^3\cdot 3\sqrt[3]{2}[/latex]
    [latex]\phantom{h(\dfrac{1}{3})}=-8\cdot 3\sqrt[3]{2}[/latex]
    [latex]\phantom{h(\dfrac{1}{3})}=-24 \sqrt[3]{2}[/latex]
  22. [latex]h(x^4)=(x^4)^2+1[/latex]
    [latex]\phantom{h(x^4)}=x^8+1[/latex]
  23. [latex]h(t^2)=(t^2)^2+t[/latex]
    [latex]\phantom{h(t^2)}=t^4+t[/latex]
  24. [latex]f(0)=|\cancel{3(0)}+1|+1[/latex]
    [latex]\phantom{f(0)}=1+1\text{ or }2[/latex]
  25. [latex]f(-6)=-2 |-(-6)-2 | +1[/latex]
    [latex]\phantom{f(-6)}=-2 |6-2| + 1[/latex]
    [latex]\phantom{f(-6)}=-2(4)+1[/latex]
    [latex]\phantom{f(-6)}=-8 + 1\text{ or }-7[/latex]
  26. [latex]f(10)=|10+3|[/latex]
    [latex]\phantom{f(10)}=13[/latex]
  27. [latex]p(5)=-|5|+1[/latex]
    [latex]\phantom{p(-5)}=-5+1[/latex]
    [latex]\phantom{p(-5)}=-4[/latex]

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