{"id":2018,"date":"2021-12-02T19:40:30","date_gmt":"2021-12-03T00:40:30","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-2\/"},"modified":"2022-11-02T10:39:10","modified_gmt":"2022-11-02T14:39:10","slug":"answer-key-11-2","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-2\/","title":{"raw":"Answer Key 11.2","rendered":"Answer Key 11.2"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ng(3)&=&(3)^3+5(3)^2 \\\\\n&=&27+45 \\\\\n&=&72\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\nf(3)&=&2(3)+4 \\\\\n&=&6+4 \\\\\n&=&10 \\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex](3)+f(3)=72+10=82[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\nf(-4)&=&-3(-4)^2+3(-4) \\\\\n&=&-3(16)-12 \\\\\n&=&-48-12 \\\\\n&=&-60\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\ng(-4)&=&2(-4)+5 \\\\\n&=&-8+5 \\\\\n&=&-3\\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex]\\dfrac{f(-4)}{g(-4)}=\\dfrac{-60}{-3}=20[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ng(5)&=&-4(5)+1 \\\\\n&=&-20+1 \\\\\n&=&-19\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\nh(5)&=&-2(5)-1 \\\\\n&=&-10-1 \\\\\n&=& -11\\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex]g(5)+h(5)=-19-11=-30[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ng(2)&=&3(2)+1 \\\\\n&=&6+1 \\\\\n&=&7\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\nf(2)&=&(2)^3+3(2)^2 \\\\\n&=&8+3\\cdot 4 \\\\\n&=&8+12 \\\\\n&=&20\\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex]g(2)\\cdot f(2)=7\\cdot 20=140[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ng(1)&=&1-3 \\\\\n&=&-2\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\nh(1)&=&-3(1)^3+6(1) \\\\\n&=&-3+6 \\\\\n&=&3\\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex]g(1)+h(1)=-2+3=1[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ng(-6)&=&(-6)^2-2 \\\\\n&=&36-2 \\\\\n&=&34\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\nh(-6)&=&2(-6)+5 \\\\\n&=&-12+5 \\\\\n&=&-7\\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex]g(-6)+h(-6)=34-7=27[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\nh(0)&=&\\cancel{2(0)}-1 \\\\\n&=&-1\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\ng(0)&=&\\cancel{3(0)}-5 \\\\\n&=&-5\n\\end{array}\n\\end{array}[\/latex]\n[latex]\\dfrac{h(0)}{g(0)}=\\dfrac{-1}{-5}=\\dfrac{1}{5}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex](g+h)=\n\\begin{array}[t]{rrrr}\n&3a&-&2 \\\\\n+&4a&-&2 \\\\\n\\hline\n&7a&-&4\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g+h)(10)&=&7(10)-4 \\\\\n&=&70-4 \\\\\n&=&66\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex](g+f)=\n\\begin{array}[t]{rrrr}\n&3a&+&3 \\\\\n+&2a&-&2 \\\\\n\\hline\n&5a&+&1\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g+f)(9)&=&5(9)+1 \\\\\n&=&45+1 \\\\\n&=&46\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex](g-h)=\n\\begin{array}[t]{r}\n4x+3 \\\\\n- \\hspace{0.42in} (x^3-2x^2) \\\\\n\\hline\n-x^3+2x^2+4x+3\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g-h)(-1)&=&-(-1)^3+2(-1)^2+4(-1)+3 \\\\\n&=&1+2-4+3 \\\\\n&=&2\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex](g-f)=\n\\begin{array}[t]{rrrr}\n&x&+&3 \\\\\n-&(-x&+&4) \\\\\n\\hline\n&2x&-&1\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g-f)(3)&=&2(3)-1 \\\\\n&=&6-1 \\\\\n&=&5\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex](g-f)=\n\\begin{array}[t]{rrrrrr}\n&x^2&&&+&2 \\\\\n-&&&(2x&+&5) \\\\\n\\hline\n&x^2&-&2x&-&3\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g-f)(0)&=&\\cancel{(0)^2}-\\cancel{2(0)}-3 \\\\\n&=&-3\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex](f+g)=\n\\begin{array}[t]{rrrr}\n&n&-&5 \\\\\n+&4n&+&2 \\\\\n\\hline\n&5n&-&3\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(f+g)(-8)&=&5(-8)-3 \\\\\n&=&-40-3 \\\\\n&=&-43\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex](h\\cdot g)=\n\\begin{array}[t]{rrrrrr}\n&&&t&+&5 \\\\\n\\times &&&3t&-&5 \\\\\n\\hline\n&3t^2&+&15t&& \\\\\n&&-&5t&-&25 \\\\\n\\hline\n&3t^2&+&10t&-&25\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(h\\cdot g)(5)&=&3(5)^2+10(5)-25 \\\\\n&=&75+50-25 \\\\\n&=&100\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex](g\\cdot h)=\n\\begin{array}[t]{rrrr}\n&t&-&4 \\\\\n\\times &&&2t \\\\\n\\hline\n&2t^2&-&8t\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g\\cdot h)(3t)&=&2(3t)^2-8(3t) \\\\\n&=&2(9t^2)-24t \\\\\n&=&18t^2-24t\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\dfrac{g(n)}{f(n)}=\\dfrac{n^2+5}{2n+5}\\hspace{0.25in} \\text{Does not reduce}[\/latex]<\/li>\n \t
  17. [latex]\\dfrac{g}{f}=\\dfrac{-2a+5}{3a+5}\\hspace{0.3in}\\left(\\dfrac{g}{f}\\right)(a^2)=\\dfrac{-2a^2+5}{3a^2+5}\\hspace{0.25in} \\text{Does not reduce}[\/latex]<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]h(n)+g(n)=\n\\begin{array}[t]{rrrrrr}\n&n^3&+&4n&& \\\\\n+&&&4n&+&5 \\\\\n\\hline\n&n^3&+&8n&+&5\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]g(n^2)=(n^2)^2-4(n^2)[\/latex]\n[latex]\\phantom{g(n^2)}=n^4-4n^2 \\hspace{1in} h(n^2)=n^2-5[\/latex]\n[latex]g(n^2)\\cdot h(n^2)=\n\\begin{array}[t]{rrrrrr}\n&&&n^4&-&4n^2 \\\\\n\\times&&&n^2&-&5 \\\\\n\\hline\n&n^6&-&4n^4&& \\\\\n&&-&5n^4&+&20n^2 \\\\\n\\hline\n&n^6&-&9n^4&+&20n^2 \\\\\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex](g\\cdot h)=\n\\begin{array}[t]{rrrrrr}\n&&&n&+&5 \\\\\n\\times &&&2n&-&5 \\\\\n\\hline\n&2n^2&+&10n&& \\\\\n&&-&5n&-&25 \\\\\n\\hline\n&2n^2&+&5n&-&25\n\\end{array}\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g\\cdot h)(-3n)&=&2(-3n)^2+5(-3n)-25 \\\\\n&=&2(9n^2)-15n-25 \\\\\n&=&18n^2-15n-25\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n(f\\circ g)&=&-4(4x+3)+1 \\\\\n&=&-16x-12+1 \\\\\n&=&-16x-11\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(f\\circ g)(9)&=&-16(9)-11 \\\\\n&=&-144-11 \\\\\n&=&-155\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n(h\\circ g)&=&3(a+1)+3 \\\\\n&=&3a+3+3 \\\\\n&=&3a+6\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(h\\circ g)(5)&=&3(5)+6 \\\\\n&=&15+6 \\\\\n&=&21\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n(g\\circ h)&=&(x^2-1)+4 \\\\\n&=&x^2-1+4 \\\\\n&=&x^2+3\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g\\circ h)(10)&=&(10)^2+3 \\\\\n&=&100+3 \\\\\n&=&103\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n(f\\circ g)&=&-4(n+4)+2 \\\\\n&=&-4n-16+2 \\\\\n&=&-4n-14\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(f\\circ g)(9)&=&-4(9)-14 \\\\\n&=&-36-14 \\\\\n&=&-50\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  25. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n(g\\circ h)&=&2(2x^3+4x^2)-4 \\\\\n&=&4x^3+8x^2-4\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrl}\n(g\\circ h)(3)&=&4(3)^3+8(3)^2-4 \\\\\n&=&108+72-4 \\\\\n&=&176\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  26. [latex](g\\circ h)=(4x+4)^2-5(4x+4) [\/latex]\n[latex]\\phantom{g\\circ h)}=16x^2+32x+16-20x-20 [\/latex]\n[latex]\\phantom{g\\circ h)}=16x^2+12x-4[\/latex]<\/li>\n \t
  27. [latex](f\\circ g)=-2(4a)+2 [\/latex]\n[latex]\\phantom{f\\circ g)}=-8a+2[\/latex]<\/li>\n \t
  28. [latex](g\\circ f)=4(x^3-1)+4[\/latex]\n[latex]\\phantom{g\\circ f)}=4x^3-4+4 [\/latex]\n[latex]\\phantom{g\\circ f)}=4x^3[\/latex]<\/li>\n \t
  29. [latex](g\\circ f)=-(2x-3)+5[\/latex]\n[latex]\\phantom{g\\circ f)}=-2x+6+5 [\/latex]\n[latex]\\phantom{g\\circ f)}=-2x+11[\/latex]<\/li>\n \t
  30. [latex](f\\circ g)=4(-4t-2)+3 [\/latex]\n[latex]\\phantom{f\\circ g)}=-16t-8+3[\/latex]\n[latex]\\phantom{f\\circ g)}=-16t-5[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} g(3)&=&(3)^3+5(3)^2 \\\\ &=&27+45 \\\\ &=&72 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} f(3)&=&2(3)+4 \\\\ &=&6+4 \\\\ &=&10 \\\\ \\end{array} \\end{array}[\/latex]
      \n[latex](3)+f(3)=72+10=82[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} f(-4)&=&-3(-4)^2+3(-4) \\\\ &=&-3(16)-12 \\\\ &=&-48-12 \\\\ &=&-60 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} g(-4)&=&2(-4)+5 \\\\ &=&-8+5 \\\\ &=&-3\\\\ \\end{array} \\end{array}[\/latex]
      \n[latex]\\dfrac{f(-4)}{g(-4)}=\\dfrac{-60}{-3}=20[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} g(5)&=&-4(5)+1 \\\\ &=&-20+1 \\\\ &=&-19 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} h(5)&=&-2(5)-1 \\\\ &=&-10-1 \\\\ &=& -11\\\\ \\end{array} \\end{array}[\/latex]
      \n[latex]g(5)+h(5)=-19-11=-30[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} g(2)&=&3(2)+1 \\\\ &=&6+1 \\\\ &=&7 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} f(2)&=&(2)^3+3(2)^2 \\\\ &=&8+3\\cdot 4 \\\\ &=&8+12 \\\\ &=&20\\\\ \\end{array} \\end{array}[\/latex]
      \n[latex]g(2)\\cdot f(2)=7\\cdot 20=140[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} g(1)&=&1-3 \\\\ &=&-2 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} h(1)&=&-3(1)^3+6(1) \\\\ &=&-3+6 \\\\ &=&3\\\\ \\end{array} \\end{array}[\/latex]
      \n[latex]g(1)+h(1)=-2+3=1[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} g(-6)&=&(-6)^2-2 \\\\ &=&36-2 \\\\ &=&34 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} h(-6)&=&2(-6)+5 \\\\ &=&-12+5 \\\\ &=&-7\\\\ \\end{array} \\end{array}[\/latex]
      \n[latex]g(-6)+h(-6)=34-7=27[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} h(0)&=&\\cancel{2(0)}-1 \\\\ &=&-1 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} g(0)&=&\\cancel{3(0)}-5 \\\\ &=&-5 \\end{array} \\end{array}[\/latex]
      \n[latex]\\dfrac{h(0)}{g(0)}=\\dfrac{-1}{-5}=\\dfrac{1}{5}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex](g+h)= \\begin{array}[t]{rrrr} &3a&-&2 \\\\ +&4a&-&2 \\\\ \\hline &7a&-&4 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g+h)(10)&=&7(10)-4 \\\\ &=&70-4 \\\\ &=&66 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex](g+f)= \\begin{array}[t]{rrrr} &3a&+&3 \\\\ +&2a&-&2 \\\\ \\hline &5a&+&1 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g+f)(9)&=&5(9)+1 \\\\ &=&45+1 \\\\ &=&46 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex](g-h)= \\begin{array}[t]{r} 4x+3 \\\\ - \\hspace{0.42in} (x^3-2x^2) \\\\ \\hline -x^3+2x^2+4x+3 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g-h)(-1)&=&-(-1)^3+2(-1)^2+4(-1)+3 \\\\ &=&1+2-4+3 \\\\ &=&2 \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex](g-f)= \\begin{array}[t]{rrrr} &x&+&3 \\\\ -&(-x&+&4) \\\\ \\hline &2x&-&1 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g-f)(3)&=&2(3)-1 \\\\ &=&6-1 \\\\ &=&5 \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex](g-f)= \\begin{array}[t]{rrrrrr} &x^2&&&+&2 \\\\ -&&&(2x&+&5) \\\\ \\hline &x^2&-&2x&-&3 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g-f)(0)&=&\\cancel{(0)^2}-\\cancel{2(0)}-3 \\\\ &=&-3 \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex](f+g)= \\begin{array}[t]{rrrr} &n&-&5 \\\\ +&4n&+&2 \\\\ \\hline &5n&-&3 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (f+g)(-8)&=&5(-8)-3 \\\\ &=&-40-3 \\\\ &=&-43 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex](h\\cdot g)= \\begin{array}[t]{rrrrrr} &&&t&+&5 \\\\ \\times &&&3t&-&5 \\\\ \\hline &3t^2&+&15t&& \\\\ &&-&5t&-&25 \\\\ \\hline &3t^2&+&10t&-&25 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (h\\cdot g)(5)&=&3(5)^2+10(5)-25 \\\\ &=&75+50-25 \\\\ &=&100 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex](g\\cdot h)= \\begin{array}[t]{rrrr} &t&-&4 \\\\ \\times &&&2t \\\\ \\hline &2t^2&-&8t \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g\\cdot h)(3t)&=&2(3t)^2-8(3t) \\\\ &=&2(9t^2)-24t \\\\ &=&18t^2-24t \\end{array}[\/latex]<\/li>\n
    16. [latex]\\dfrac{g(n)}{f(n)}=\\dfrac{n^2+5}{2n+5}\\hspace{0.25in} \\text{Does not reduce}[\/latex]<\/li>\n
    17. [latex]\\dfrac{g}{f}=\\dfrac{-2a+5}{3a+5}\\hspace{0.3in}\\left(\\dfrac{g}{f}\\right)(a^2)=\\dfrac{-2a^2+5}{3a^2+5}\\hspace{0.25in} \\text{Does not reduce}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]h(n)+g(n)= \\begin{array}[t]{rrrrrr} &n^3&+&4n&& \\\\ +&&&4n&+&5 \\\\ \\hline &n^3&+&8n&+&5 \\end{array}[\/latex]<\/li>\n
    19. [latex]g(n^2)=(n^2)^2-4(n^2)[\/latex]
      \n[latex]\\phantom{g(n^2)}=n^4-4n^2 \\hspace{1in} h(n^2)=n^2-5[\/latex]
      \n[latex]g(n^2)\\cdot h(n^2)= \\begin{array}[t]{rrrrrr} &&&n^4&-&4n^2 \\\\ \\times&&&n^2&-&5 \\\\ \\hline &n^6&-&4n^4&& \\\\ &&-&5n^4&+&20n^2 \\\\ \\hline &n^6&-&9n^4&+&20n^2 \\\\ \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex](g\\cdot h)= \\begin{array}[t]{rrrrrr} &&&n&+&5 \\\\ \\times &&&2n&-&5 \\\\ \\hline &2n^2&+&10n&& \\\\ &&-&5n&-&25 \\\\ \\hline &2n^2&+&5n&-&25 \\end{array}\\hspace{0.25in} \\begin{array}[t]{rrl} (g\\cdot h)(-3n)&=&2(-3n)^2+5(-3n)-25 \\\\ &=&2(9n^2)-15n-25 \\\\ &=&18n^2-15n-25 \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} (f\\circ g)&=&-4(4x+3)+1 \\\\ &=&-16x-12+1 \\\\ &=&-16x-11 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} (f\\circ g)(9)&=&-16(9)-11 \\\\ &=&-144-11 \\\\ &=&-155 \\end{array} \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} (h\\circ g)&=&3(a+1)+3 \\\\ &=&3a+3+3 \\\\ &=&3a+6 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} (h\\circ g)(5)&=&3(5)+6 \\\\ &=&15+6 \\\\ &=&21 \\end{array} \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} (g\\circ h)&=&(x^2-1)+4 \\\\ &=&x^2-1+4 \\\\ &=&x^2+3 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} (g\\circ h)(10)&=&(10)^2+3 \\\\ &=&100+3 \\\\ &=&103 \\end{array} \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} (f\\circ g)&=&-4(n+4)+2 \\\\ &=&-4n-16+2 \\\\ &=&-4n-14 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} (f\\circ g)(9)&=&-4(9)-14 \\\\ &=&-36-14 \\\\ &=&-50 \\end{array} \\end{array}[\/latex]<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} (g\\circ h)&=&2(2x^3+4x^2)-4 \\\\ &=&4x^3+8x^2-4 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrl} (g\\circ h)(3)&=&4(3)^3+8(3)^2-4 \\\\ &=&108+72-4 \\\\ &=&176 \\end{array} \\end{array}[\/latex]<\/li>\n
    26. [latex](g\\circ h)=(4x+4)^2-5(4x+4)[\/latex]
      \n[latex]\\phantom{g\\circ h)}=16x^2+32x+16-20x-20[\/latex]
      \n[latex]\\phantom{g\\circ h)}=16x^2+12x-4[\/latex]<\/li>\n
    27. [latex](f\\circ g)=-2(4a)+2[\/latex]
      \n[latex]\\phantom{f\\circ g)}=-8a+2[\/latex]<\/li>\n
    28. [latex](g\\circ f)=4(x^3-1)+4[\/latex]
      \n[latex]\\phantom{g\\circ f)}=4x^3-4+4[\/latex]
      \n[latex]\\phantom{g\\circ f)}=4x^3[\/latex]<\/li>\n
    29. [latex](g\\circ f)=-(2x-3)+5[\/latex]
      \n[latex]\\phantom{g\\circ f)}=-2x+6+5[\/latex]
      \n[latex]\\phantom{g\\circ f)}=-2x+11[\/latex]<\/li>\n
    30. [latex](f\\circ g)=4(-4t-2)+3[\/latex]
      \n[latex]\\phantom{f\\circ g)}=-16t-8+3[\/latex]
      \n[latex]\\phantom{f\\circ g)}=-16t-5[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":108,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2018","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2018","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2018\/revisions"}],"predecessor-version":[{"id":2019,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2018\/revisions\/2019"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2018\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2018"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2018"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2018"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2018"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}