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

Jika , dan , maka tentukan:

b.  

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Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses h ring operator g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator negative 36 x squared minus 120 x minus 99 over denominator 36 x squared plus 120 x plus 100 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 h ring operator g ring operator f close parentheses open parentheses x close parentheses end style.

Terlebih dahulu tentukan begin mathsize 14px style open parentheses g ring operator f 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 g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 2 x plus 3 close parentheses end cell row blank equals cell fraction numerator 1 over denominator 3 open parentheses 2 x plus 3 close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator 1 over denominator 6 x plus 9 plus 1 end fraction end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator 6 x plus 10 end fraction end cell end table end style 

Sehingga begin mathsize 14px style open parentheses h ring operator g ring operator f 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 h ring operator g ring operator f close parentheses open parentheses x close parentheses end cell equals cell h open parentheses open parentheses g ring operator f close parentheses open parentheses x close parentheses close parentheses end cell row blank equals cell h open parentheses fraction numerator 1 over denominator 6 x plus 10 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 over denominator 6 x plus 10 end fraction close parentheses squared minus 1 end cell row blank equals cell fraction numerator 1 over denominator 36 x squared plus 120 x plus 100 end fraction minus 1 end cell row blank equals cell fraction numerator 1 minus 1 open parentheses 36 x squared plus 120 x plus 100 close parentheses over denominator 36 x squared plus 120 x plus 100 end fraction end cell row blank equals cell fraction numerator 1 minus 36 x squared minus 120 x minus 100 over denominator 36 x squared plus 120 x plus 100 end fraction end cell row cell open parentheses h ring operator g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator negative 36 x squared minus 120 x minus 99 over denominator 36 x squared plus 120 x plus 100 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 h ring operator g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator negative 36 x squared minus 120 x minus 99 over denominator 36 x squared plus 120 x plus 100 end fraction end cell end table end style.

46

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