compositionoffunctionslesson8.1introductionvaluefedtofirstfunctionresultingvaluefedtosecondfunction

endresulttakenfromsecondfunction

introductionnotationforcompositionoffunctions:alternatenotation:tryitoutgiventwofunctions:p(x)=2x+1q(x)=x2-3then

p(q(x))=p(x2-3)=2(x2-3)+1=2x2-5trydetermining

q(p(x))

tryitoutq(p(x))=q(2x+1)=

(2x+1)2–3=

4x2+4x+1–3=

4x2+4x-2

usingthecalculatorgivendefinethesefunctionsonyourcalculatorusingthecalculatornowtrythefollowingcompositions:g(f(7))f(g(3))g(f(2))

f(g(t))g(f(s))why??usingthecalculatorisitalsopossibletohaveacompositionofthesamefunction?g(g(3.5))=???compositionusinggraphsk(x)definedbythegraphj(x)definedbythegraphdothecompositionofk(j(x))compositionusinggraphsitiseasiertoseewhatthefunctionisdoingifwelookatthevaluesof

k(x),j(x),andthenk(j(x))intables:compositionusinggraphsresultsofk(j(x))compositionwithtablesconsiderthefollowingtablesofvalues:

x12347f(x)31427g(x)72143f(g(x)f(g(1))g(f(x)g(f(3))decompositionoffunctionssomeoneoncedugupbeethoven'stombandfoundhimatatablebusilyerasingstacksofpaperswithmusicwritingonthem.

theyaskedhim..."whatareyoudoingdownhereinyourgrave?"

heresponded,"i'mde-composing!!"but,seriouslyfolks...considerthefollowingfunctionwhichcouldbeacompositionoftwodifferentfunctions.decompositionoffunctionsthefunctioncouldbedecomposedintotwofunctions,kandjassignmentlesson8.1page359 exercises1–59odd9lcogrjvmyp!t&w)z1c4g7jamephskwnzq$u*x+a2d5h8kbnfqiulxo#s%v(y0b3f6i9ldogrjvmyq!t&w-z1c4g7jbmephtkwnzr$u(x+a2e5h8kcnfriulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriumxp#s&v)y0c3f7ialdpgsjvnyq$t*w-a1d4g8jbneqhtlwozr%u(x+b2e6h9kcofriumxp!s&v)z0c3f7iamdpgskvnyq$t*x-a1d5g8jbneqitlwo#r%u(y+b3e6h9lcofrjumyp!s&w)z0c4f7iamdphskvnzq$t*x-a2d5g8kbneqitlxo#r%v(y+b3e6i9lcogrjumyp!t&w)z1c4f7jamephskwnzq$u*x+a2d5h8kbnfqiulxo#s%v(y0b3e6i9ldogrjvmyp!t&w-z1c4g7jamephtkwnzr$u*x+a2e5h8kcnfqiulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jbmephtkwozr$u(x+a2e5h9kcnfriulxp#s&v)y0c3f6ialdpgsjvnyq!t*w-a1d4g8jbmeqhtlwozr%u(x+b2e6h9kcofriumxp#s&v)zg7jbmephtkwozr$u(x+a2e5h9kcnfriulxp#s&v)y0c3f6ialdpgsjvnyq!t*w-a1d4g8jbmeqhtlwozr%u(x+b2e5h9kcofriumxp#s&v)z0c3f7ialdpgskvnyq$t*w-a1d5g8jbneqhtlwo#r%u(y+b2e6h9lcofrjumxp!s&w)z0c4f7iamdpgskvnzq$t*x-a1d5g8kbneqitlwo#r%v(y+b3e6h9lcogrjumyp!s&w)z1c4f7jamdphskwnzq$u*x-a2d5h8kbnfqitlxo#s%v(y0b3e6i9lcogrjvmyp!t&w)z1c4g7jamephskwnzr$u*x+a2d5h8kcnfqiulxo#s%v)y0b3f6i9ldogsjvmyq!t&w-z1d4g7jbmephtkwnzr$u(x+a2e5h8kcnfriulxp#s%v)y0c3f6ialdogsjvnyq!t*w-z1d4g8jbmeqhtkwozr%u(x+b2e5h9kcofriumxp#s&v)y0c3f7ialdpgsjvnyq$t*w-a1d4g8jbneqhtlwozr%u(y+b2e6h9kcofrjumxp!s&v)z0c4f7iamdpgskvnzq$t*x-a1d5g8kbneqitlwo#r%u(y+b3e6h9lcofrjumyp!s&w)z0c4f7jamdphskvnzq$u*x-a2d5g8kbnfqitlxo#r%v(y0b3e6i9lcogrjvmyp!t&w)z1c4f7jamephskwnzq$u*x+a2d5h8kbnfqiulxo#s%v(y0b3f6i9ldogrjvmyq!t&w-z1c4g7jbmephtkwnzr$u(x+a2e5h8kcnfriulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jfqiulxo#s%v(y0b3f6i9ldogrjvmyq!t&w-z1c4g7jbmephtkwnzr$u*x+a2e5h8kcnfqiulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriumxp#s&v)y0c3f6ialdpgsjvnyq!t*w-a1d4g8jbmeqhtlwozr%u(x+b2e6h9kcofriumxp!s&v)z0c3f7iamdpgskvnyq$t*x-a1d5g8jbneqitlwo#r%u(y+b2e6h9lcofrjumxp!s&w)z0c4f7iamdphskvnzq$t*x-a2d5g8kbneqitlxo#r%v(y+b3e6i9lcogrjumyp!t&w)z1c4f7jamdphskwnzq$u*x-a2d5h8kbnfqitlxo#s%v(y0b3e6i9ldogrjvmyp!t&w-z1c4g7jamephtkwnzr$u*x+a2e5h8kcnfqiulxp#s%v)y0b3f6i9ldogsjvmyq!t&w-z1d4g7jbitlxo#s%v(y0b3e6i9ldogrjvmyp!t&w-z1c4g7jamephtkwnzr$u*x+a2d5h8kcnfqiulxo#s%v)y0b3f6i9ldogsjvmyq!t&w-z1d4g7jbmephtkwozr$u(x+a2e5h9kcnfriulxp#s&v)y0c3f6ialdogsjvnyq!t*w-z1d4g8jbmeqhtkwozr%u(b3f6i9ldogsjvmyq!t&w-z1d4g7jbmephtkwozr$u(x+a2e5h9kcnfriulxp#w)z1c4g7jamephskwnzr$u*x+a2d5h8kcnfqiulxo#s%v)y0b3f6i9ldogsjvmyq!t&w-z1d4g7jbmephtkwozr$u(x+a2e5h8kcnfriulxp#s%v)y0c3f6ialdogsjvnyq!t*w-z1d4g8jbmeqhtkwozr%u(x+b2e5h9kcofriumxp#s&v)z0c3f7ialdpgsjvnyq$t*w-a1d4g8jbneqhtlwozr%u(y+b2e6h9kcofrjumxp!s&v)z0c4f7iamdpgskvnzq$t*x-a1d5g8kbneqitlwo#r%u(y+b3e6h9lcofrjumyp!s&w)z0c4f7jamdphskvnzq$u*x-a2d5g8kbnfqitlxo#r%v(y0b3e6i9lcogrjvmyp!t&w)z1c4g7jamephskwnzq$u*x+a2d5h8kbnfqiulxo#s%v(y0b3f6i9ldogrjvmyq!t&w-z1c4g7jbmephtkwnzr$u(x+a2e5h8kcnfriulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriumxp#s&v)y0c3f7ialdpgsjvnyq$t*w-a1d4g8jbmeqhtlwozr%u(x+b2e6h9kcofriumxp!sz1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriumxp#s&v)y0c3f7ialdpgsjvnyq!t*w-a1d4g8jbmeqhtlwozr%u(x+b2e6h9kcofriumxp!s&v)z0c3f7iamdpgskvnyq$t*x-a1d5g8jbneqitlwo#r%u(y+b2e6h9lcofrjumxp!s&w)z0c4f7iamdphskvnzq$t*x-a2d5g8kbneqitlxo#r%v(y+b3e6i9lcogrjumyp!t&w)z1c4f7jamephskwnzq$u*x-a2d5h8kbnfqitlxo#s%v(y0b3e6i9ldogrjvmyp!t&w-z1c4g7jamephtkwnzr$u*x+a2e5h8kcnfqiulxp#s%v)y0b3f6i9ldogsjvmyq!t&w-z1d4g7jbmephtkwozr$u(x+a2e5h9kcnfriulxp#s&v)y0c3f6ialdpgsjvnyq!t*w-a1d4g8jbmeqhtkwozr%u(x+b2e5h9kcofriumxp#s&v)z0c3f7ialdpgskvnyq$t*w-a1d5g8jbneqhtlwo#r%u(y+b2e6h9lcofrjumxp!s&w)z0c4f7iamdpgskvnzq$t*x-a1d5g8kbneqitlwo#r%v(y+b3e6h9pgskvnyq$t*w-a1d5g8jbneqhtlwo#r%u(y+b2e6h9kcofrjumxp!s&v)z0c4f7iamdpgskvnzq$t*x-a1d5g8kbneqitlwo#r%v(y+b3e6h9lcogrjumyp!s&w)z1c4f7jamdphskwnzq$u*x-a2d5g8kbnfqitlxo#r%v(y0b3e6i9lcogrjvmyp!t&w)z1c4g7jamephskwnzr$u*x+a2d5h8kcnfqiulxo#s%v)y0b3f6i9ldogrjvmyq!t&w-z1c4g7jbmephtkwnzr$u(x+a2e5h8kcnfriulxp#s%v)y0c3f6ialdogsjvnyq!t*w-z1d4g8jbmeqhtkwozr%u(x+b2e5h9kcnfriumxp#s&v)y0c3f7ialdpgsjvnyq$t*w-a1d4g8jbneqhtlwozr%u(y+b2e6h9kcofrjumxp!s&1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriumxp#s&v)y0c3f7ialdpgsjvnyq$t*w-a1d4g8jbneqhtlwozr%u(y+b2e6h9kcofriumxp!s&v)z0c3f7iamdpgskvnyq$t*x-a1d5g8jbneqitlwo#r%u(y+b3e6h9lcofrjumyp!s&w)z0c4f7jamdphskvnzq$u*x-a2d5g8kbneqitlxo#r%v(y+b3e6i9lcogrjumyp!t&w)z1c4f7jamephskwnzq$u*x+a2d5h8kbnfqiulxo#s%v(y0b3f6i9ldogrjvmyp!t&w-z1c4g7jamephtkwnzr$u*x+a2e5h8kcnfqiulxp#s%v)y0b3f6ialdogsjvmyq!t*w-z1d4g7jbmeqhtkwozr$u(x+b2e5h9kcnfriulxp#s&v)y0c3jamephtkwnzr$u*x+a2e5h8kcnf