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Diketahui nilai , , dan . Nilai dari  adalah ....

Pertanyaan

Diketahui nilai begin mathsize 14px style f open parentheses x close parentheses equals 4 x end stylebegin mathsize 14px style g open parentheses x close parentheses equals 9 x plus 2 end style, dan begin mathsize 14px style h open parentheses x close parentheses equals 9 minus x end style. Nilai dari begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style adalah ....

Pembahasan Soal:

Gunakan konsep invers fungsi komposisi tiga fungsi.

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

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals 4 x end stylebegin mathsize 14px style g open parentheses x close parentheses equals 9 x plus 2 end style, dan begin mathsize 14px style h open parentheses x close parentheses equals 9 minus x end style

Akan ditentukan nilai dari begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style.

Terlebih dahulu tentukan begin mathsize 14px style g to the power of negative 1 end exponent open parentheses x close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell g open parentheses x close parentheses equals y end cell equals cell 9 x plus 2 end cell row cell y minus 2 end cell equals cell 9 x end cell row cell 9 x end cell equals cell y minus 2 end cell row x equals cell fraction numerator y minus 2 over denominator 9 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator 9 end fraction end cell end table end style 

Menentukan nilai begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style, perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell open parentheses open parentheses h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator open parentheses f to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell row blank equals cell open parentheses h ring operator g to the power of negative 1 end exponent ring operator f close parentheses open parentheses x close parentheses end cell row blank equals cell h ring operator open parentheses open parentheses g to the power of negative 1 end exponent ring operator f close parentheses open parentheses x close parentheses close parentheses end cell row blank equals cell h ring operator open parentheses g to the power of negative 1 end exponent open parentheses 4 x close parentheses close parentheses end cell row blank equals cell h ring operator open parentheses fraction numerator 4 x minus 2 over denominator 9 end fraction close parentheses end cell row blank equals cell 9 minus open parentheses fraction numerator 4 x minus 2 over denominator 9 end fraction close parentheses end cell row blank equals cell fraction numerator 81 minus 4 x plus 2 over denominator 9 end fraction end cell row cell open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 4 x plus 83 over denominator 9 end fraction end cell end table end style 

Jadi, diperoleh nilai begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g ring operator h to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 4 x plus 83 over denominator 9 end fraction end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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