Jika g(x+1)=2x−7,nilai x yang memenuhi (g∘g)−1(x)=26x−3​ adalah ....

Pertanyaan

Jika begin mathsize 14px style g open parentheses x plus 1 close parentheses equals 2 x minus 7 end style,nilai begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style open parentheses g ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 x minus 3 over denominator 2 end fraction end style adalah ....

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

nilai x yang memenuhi adalah begin mathsize 14px style 33 over 13 end style.

Pembahasan

  • Mencari begin mathsize 14px style g open parentheses x close parentheses end style dari begin mathsize 14px style g open parentheses x plus 1 close parentheses equals 2 x minus 7 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses y close parentheses end cell equals cell 2 open parentheses y minus 1 close parentheses minus 7 end cell row cell g open parentheses y close parentheses end cell equals cell 2 y minus 9 end cell row blank blank blank end table end style

Jadi, diperoleh begin mathsize 14px style g open parentheses x close parentheses equals 2 x minus 9 end style.

  • Mencari begin mathsize 14px style open parentheses g ring operator g close parentheses open parentheses x close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator g close parentheses open parentheses x close parentheses end cell equals cell g open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 2 x minus 9 close parentheses end cell row blank equals cell 2 open parentheses 2 x minus 9 close parentheses minus 9 end cell row blank equals cell 4 x minus 18 minus 9 end cell row blank equals cell 4 x minus 27 end cell end table end style

  • Mencari begin mathsize 14px style left parenthesis g ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style

Misal begin mathsize 14px style left parenthesis g ring operator g right parenthesis left parenthesis x right parenthesis equals y end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus 27 end cell equals y row cell 4 x end cell equals cell y plus 27 end cell row x equals cell fraction numerator y plus 27 over denominator 4 end fraction end cell row blank blank blank row cell open parentheses g ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 27 over denominator 4 end fraction end cell end table end style

  • Karena begin mathsize 14px style open parentheses g ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 x minus 3 over denominator 2 end fraction end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 27 over denominator 4 end fraction end cell equals cell fraction numerator 6 x minus 3 over denominator 2 end fraction end cell row cell 4 open parentheses fraction numerator x plus 27 over denominator 4 end fraction close parentheses end cell equals cell 4 open parentheses fraction numerator 6 x minus 3 over denominator 2 end fraction close parentheses end cell row cell x plus 27 end cell equals cell 2 open parentheses 6 x minus 3 close parentheses end cell row cell x plus 27 end cell equals cell 12 x minus 6 end cell row cell x minus 12 x end cell equals cell negative 6 minus 27 end cell row cell negative 13 x end cell equals cell negative 33 end cell row x equals cell 33 over 13 end cell end table end style

Jadi, nilai x yang memenuhi adalah begin mathsize 14px style 33 over 13 end style.

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