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Jika f ( x ) = 2 x + 3 , g ( x ) = 3 x + 1 1 ​ , dan h ( x ) = x 2 − 1 , maka tentukan: a. ( f ∘ g ∘ h ) ( x )

Jika , dan , maka tentukan:

a.  

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Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

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Jawaban

diperoleh .

diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 9 x squared minus 4 over denominator 3 x squared minus 2 end fraction end cell end table end style.

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Pembahasan

Gunakan konsep fungsi komposisi. Diketahui: Akan ditentukan ​​​​​​ . Terlebih dahulu tentukan , diperoleh: Sehingga diperoleh: Jadi, diperoleh .

Gunakan konsep fungsi komposisi.

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 3 end style

begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 1 over denominator 3 x plus 1 end fraction end style

begin mathsize 14px style h open parentheses x close parentheses equals x squared minus 1 end style

Akan ditentukan ​​​​​​begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end style.

Terlebih dahulu tentukan begin mathsize 14px style open parentheses g ring operator h close parentheses open parentheses x close parentheses end style, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis h open parentheses x close parentheses right parenthesis end cell row blank equals cell g left parenthesis x squared minus 1 right parenthesis end cell row blank equals cell fraction numerator 1 over denominator 3 left parenthesis x squared minus 1 right parenthesis plus 1 end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 x squared minus 3 plus 1 end fraction end cell row cell left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 1 over denominator 3 x squared minus 2 end fraction end cell end table end style  

Sehingga begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end style diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g ring operator h close parentheses end cell row blank equals cell f open parentheses fraction numerator 1 over denominator 3 x squared minus 2 end fraction close parentheses end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator 3 x squared minus 2 end fraction close parentheses plus 3 end cell row blank equals cell fraction numerator 2 over denominator 3 x squared minus 2 end fraction plus fraction numerator 3 open parentheses 3 x squared minus 2 close parentheses over denominator 3 x squared minus 2 end fraction end cell row blank equals cell fraction numerator 2 plus 9 x squared minus 6 over denominator 3 x squared minus 2 end fraction end cell row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 9 x squared minus 4 over denominator 3 x squared minus 2 end fraction end cell end table end style 

Jadi, diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 9 x squared minus 4 over denominator 3 x squared minus 2 end fraction end cell end table end style.

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