Pertanyaan

Diketahui f(x) = 3x - 1, g(x) = x - 2, dan h(x) = 2x + 4 dengan , maka ...

$begin mathsize 14px style fraction numerator x minus 5 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator x minus 6 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator x plus 5 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator x plus 2 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator x minus 2 over denominator 6 end fraction end style$

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Pembahasan

Pertama, kita cari masing-masing invers dari f,g, dan h. Sehingga

Pertama, kita cari masing-masing invers dari f,g, dan h.

$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 3 x minus 1 end cell row y equals cell 3 x minus 1 end cell row cell y plus 1 end cell equals cell 3 x end cell row cell fraction numerator y plus 1 over denominator 3 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 plus 1 over denominator 3 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 plus 1 over denominator 3 end fraction end cell row blank blank blank row cell g open parentheses x close parentheses end cell equals cell x minus 2 end cell row y equals cell x minus 2 end cell row cell y plus 2 end cell equals x 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 y plus 2 end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell x plus 2 end cell row blank blank blank row cell h open parentheses x close parentheses end cell equals cell 2 x plus 4 end cell row y equals cell 2 x plus 4 end cell row cell y minus 4 end cell equals cell 2 x end cell row cell fraction numerator y minus 4 over denominator 2 end fraction end cell equals x 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 minus 4 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 minus 4 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 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 row blank equals 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 row blank equals 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 plus 1 over denominator 3 end fraction close parentheses close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses open parentheses fraction numerator x plus 1 over denominator 3 end fraction close parentheses plus 2 close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator x plus 1 over denominator 3 end fraction plus 6 over 3 close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator x plus 7 over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses fraction numerator x plus 7 over denominator 3 end fraction close parentheses minus 4 over denominator 2 end fraction end cell row blank equals cell fraction numerator fraction numerator x plus 7 over denominator 3 end fraction minus 12 over 3 over denominator 2 end fraction end cell row blank equals cell fraction numerator fraction numerator x minus 5 over denominator 3 end fraction over denominator 2 end fraction end cell row blank equals cell fraction numerator x minus 5 over denominator 2 times 3 end fraction end cell row blank equals cell fraction numerator x minus 5 over denominator 6 end fraction end cell end table end style$

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