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Diketahui: f(x)=5x+7g(x)=−2x+1h(x)=7x+1  Tentukan ((f∘g)∘h)−1(x)=…

Pertanyaan

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals 5 x plus 7 g open parentheses x close parentheses equals negative 2 x plus 1 h open parentheses x close parentheses equals 7 x plus 1 end style 

Tentukan begin mathsize 14px style open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals horizontal ellipsis end style 

  1. begin mathsize 14px style fraction numerator x plus 2 over denominator 70 end fraction end style 

  2. begin mathsize 14px style fraction numerator x minus 2 over denominator 70 end fraction end style 

  3. fraction numerator size 14px minus size 14px x size 14px minus size 14px 2 over denominator size 14px 70 end fraction 

  4. fraction numerator size 14px x size 14px minus size 14px 2 over denominator size 14px minus size 14px 70 end fraction 

  5. fraction numerator size 14px minus size 14px x size 14px minus size 14px 2 over denominator size 14px minus size 14px 70 end fraction 

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals 5 x plus 7 g open parentheses x close parentheses equals negative 2 x plus 1 h open parentheses x close parentheses equals 7 x plus 1 end style

Langkah-langkah mencari begin mathsize 14px style left parenthesis open parentheses f ring operator g close parentheses ring operator h right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style sebagai berikut:

1. mencari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style dengan memasukkan begin mathsize 14px style g open parentheses x close parentheses end style ke dalam fungsi begin mathsize 14px style f open parentheses x close parentheses end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses negative 2 x plus 1 close parentheses end cell row blank equals cell 5 open parentheses negative 2 x plus 1 close parentheses plus 7 end cell row blank equals cell negative 10 x plus 5 plus 7 end cell row blank equals cell negative 10 x plus 12 end cell end table end style 

2. mencari begin mathsize 14px style open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses open parentheses x close parentheses end style dengan memasukkan begin mathsize 14px style h open parentheses x close parentheses end style ke dalam fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style, yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses open parentheses x close parentheses end cell equals cell open parentheses f ring operator g close parentheses open parentheses h open parentheses x close parentheses close parentheses end cell row blank equals cell open parentheses f ring operator g close parentheses open parentheses 7 x plus 1 close parentheses end cell row blank equals cell negative 10 open parentheses 7 x plus 1 close parentheses plus 12 end cell row blank equals cell negative 70 x minus 10 plus 12 end cell row blank equals cell negative 70 x plus 2 end cell row blank blank blank end table end style 

3. mencari begin mathsize 14px style left parenthesis open parentheses f ring operator g close parentheses ring operator h right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style, yaitu

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

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses open parentheses x close parentheses end cell equals cell negative 70 x plus 2 end cell row y equals cell negative 70 x plus 2 end cell row cell negative 70 x end cell equals cell y minus 2 end cell row x equals cell fraction numerator y minus 2 over denominator negative 70 end fraction end cell row cell open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y minus 2 over denominator negative 70 end fraction end cell row cell open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator negative 70 end fraction end cell end table end style 

Oleh karena itu, jawaban yang tepat adalah D.

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