Pertanyaan

Jika f(x) = 4x + 2, g(x) = p - x, h(x) = 2x - 1 dengan , maka nilai p yang memenuhi adalah ....

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Pertama, kita caru masing-masing Sehingga

Pertama, kita caru masing-masing

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 4 x plus 2 end cell row y equals cell 4 x plus 2 end cell row cell y minus 2 end cell equals cell 4 x end cell row cell fraction numerator y minus 2 over denominator 4 end fraction end cell equals x row cell f open parentheses x close parentheses end cell equals y row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y minus 2 over denominator 4 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator 4 end fraction end cell row blank blank blank row cell g open parentheses x close parentheses end cell equals cell p minus x end cell row y equals cell p minus x end cell row x equals cell p minus y end cell row blank blank blank row cell g open parentheses x close parentheses end cell equals y row cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell p minus y end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell p minus x end cell row blank blank blank row cell h open parentheses x close parentheses end cell equals cell 2 x minus 1 end cell row y equals cell 2 x minus 1 end cell row cell y plus 1 end cell equals cell 2 x end cell row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals x row blank blank blank row cell h open parentheses x close parentheses end cell equals y row cell h to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell h to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y plus 1 over denominator 2 end fraction end cell row cell h to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 1 over denominator 2 end fraction end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g ring operator h close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell open parentheses h ring operator g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell row cell open parentheses h to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell row cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses h to the power of negative 1 end exponent open parentheses x close parentheses close parentheses close parentheses end cell row cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses fraction numerator x minus 2 over denominator 4 end fraction close parentheses close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses fraction numerator x plus 1 over denominator 2 end fraction close parentheses blank close parentheses end cell row cell h to the power of negative 1 end exponent open parentheses p minus open parentheses fraction numerator x minus 2 over denominator 4 end fraction close parentheses close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses p minus open parentheses fraction numerator x plus 1 over denominator 2 end fraction close parentheses close parentheses end cell row cell h to the power of negative 1 end exponent open parentheses fraction numerator 4 p over denominator 4 end fraction minus fraction numerator x minus 2 over denominator 4 end fraction close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses fraction numerator 2 p over denominator 2 end fraction minus fraction numerator x plus 1 over denominator 2 end fraction close parentheses end cell row cell h to the power of negative 1 end exponent open parentheses fraction numerator 4 p minus x plus 2 over denominator 4 end fraction close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses fraction numerator 2 p minus x minus 1 over denominator 2 end fraction close parentheses end cell row cell fraction numerator open parentheses fraction numerator 4 p minus x plus 2 over denominator 4 end fraction close parentheses plus 1 over denominator 2 end fraction end cell equals cell fraction numerator open parentheses fraction numerator 2 p minus x minus 1 over denominator 2 end fraction close parentheses minus 2 over denominator 4 end fraction end cell row cell fraction numerator fraction numerator 4 p minus x plus 2 over denominator 4 end fraction plus 4 over 4 over denominator 2 end fraction end cell equals cell fraction numerator fraction numerator 2 p minus x minus 1 over denominator 2 end fraction minus 4 over 2 over denominator 4 end fraction end cell row cell fraction numerator 4 p minus x plus 6 over denominator 4 times 2 end fraction end cell equals cell fraction numerator 2 p minus x minus 5 over denominator 4 times 2 end fraction end cell row cell 4 p minus x plus 6 end cell equals cell 2 p minus x minus 5 end cell row cell 4 p minus 2 p minus x plus x end cell equals cell negative 5 minus 6 end cell row cell 2 p end cell equals cell negative 11 end cell row p equals cell negative 11 over 2 end cell end table end style$

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