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Jika dan , maka

Jika begin mathsize 14px style straight f open parentheses 2 straight x minus 3 close parentheses equals negative 12 straight x plus 6 end style dan begin mathsize 14px style straight g open parentheses straight x plus 2 close parentheses equals straight x squared minus 2 straight x plus 3 end style, maka begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses equals... end style

  1. begin mathsize 14px style 36 straight x squared plus 180 straight x plus 227 end style 

  2. begin mathsize 14px style negative 6 straight x squared plus 36 straight x minus 78 end style 

  3. begin mathsize 14px style 144 straight x squared minus 120 straight x plus 27 end style 

  4. begin mathsize 14px style negative 12 straight x squared plus 24 straight x minus 30 end style 

  5. begin mathsize 14px style negative 6 straight x squared plus 180 straight x minus 30 end style 

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Pembahasan

Pertama, kita cari f (x) dan g (x). Perhatikan bahwa Sehingga Jadi,

Pertama, kita cari f (x) dan g (x).

Perhatikan bahwa

begin mathsize 14px style straight f open parentheses 2 straight x minus 3 close parentheses equals negative 12 straight x plus 6 straight f open parentheses 2 straight x minus 3 close parentheses equals negative 12 straight x plus 18 minus 12 straight f open parentheses 2 straight x minus 3 close parentheses equals negative 6 open parentheses 2 straight x minus 3 close parentheses minus 12 end style

begin mathsize 14px style straight g open parentheses straight x plus 2 close parentheses equals straight x squared minus 2 straight x plus 3 straight g open parentheses straight x plus 2 close parentheses equals straight x squared plus 4 straight x minus 6 straight x plus 4 minus 1 straight g open parentheses straight x plus 2 close parentheses equals straight x squared plus 4 straight x plus 4 minus 6 straight x minus 1 straight g open parentheses straight x plus 2 close parentheses equals open parentheses straight x squared plus 4 straight x plus 4 close parentheses minus 6 straight x minus 12 plus 11 straight g open parentheses straight x plus 2 close parentheses equals open parentheses straight x plus 2 close parentheses squared minus 6 open parentheses straight x plus 2 close parentheses plus 11 end style 

Sehingga

begin mathsize 14px style straight f open parentheses straight x close parentheses equals negative 6 straight x minus 12 straight g open parentheses straight x close parentheses equals straight x squared minus 6 straight x plus 11 end style

Jadi,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end cell equals cell straight f open parentheses straight g open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight f open parentheses straight x squared minus 6 straight x plus 11 close parentheses end cell row blank equals cell negative 6 open parentheses straight x squared minus 6 straight x plus 11 close parentheses minus 12 end cell row blank equals cell negative 6 straight x squared plus 36 straight x minus 66 minus 12 end cell row blank equals cell negative 6 straight x squared plus 36 straight x minus 78 end cell end table end style 

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Diketahui f ( x ) = x − 2 dan g ( x ) = 3 x + 1 . Jika ( f ∘ g ) ( 1 ) , ( f ∘ g ) ( k ) ,dan ( f ∘ g ) ( 3 ) membentuk suatu barisan aritmetika, maka nilai k yang mungkin adalah ....

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