Pertanyaan

Diketahui nilai f ( x ) = 4 x , g ( x ) = 9 x + 2 , dan h ( x ) = 9 − x . Nilai dari ( f − 1 ∘ g ∘ h − 1 ) − 1 ( x ) adalah ....

Diketahui nilai $f (x) = 4 x$ , $g (x) = 9 x + 2$ , dan $h (x) = 9 - x$ . Nilai dari $(f^{- 1} \circ g \circ h^{- 1})^{- 1} (x)$ adalah ....

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

diperoleh nilai .

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

Gunakan konsep invers fungsi komposisi tiga fungsi. Diketahui: , , dan Akan ditentukan nilai dari . Terlebih dahulu tentukan . Menentukan nilai , perhatikan perhitungan berikut. Jadi, diperoleh nilai .

Gunakan konsep invers fungsi komposisi tiga fungsi.

Diketahui:

, , dan

Akan ditentukan nilai dari .

Terlebih dahulu tentukan .

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

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