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Jika , , dan , maka tentukan: b.

Pertanyaan

Jika begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 3 end stylebegin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 1 over denominator 3 x plus 1 end fraction end style, dan begin mathsize 14px style h open parentheses x close parentheses equals x squared minus 1 end style, maka tentukan:

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

Pembahasan Soal:

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.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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