Roboguru

Diketahui . Jika , tentukanlah .

Diketahui begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end style. Jika begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 2 end style, tentukanlah begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style.

Jawaban:

Gunakan sifat invers fungsi komposisi dan rumus praktis invers fungsi berikut:

begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals open parentheses 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 f open parentheses x close parentheses equals a x plus b rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus b over denominator a end fraction end style  

Diketahui:
begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end style

begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 2 end style

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

Tentukan terlebih dahulu begin mathsize 14px style g to the power of negative 1 end exponent open parentheses x close parentheses end style dengan menggunakan rumus praktis, diperoleh:

begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 2 rightwards double arrow g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 2 over denominator 3 end fraction end style 

Sehingga diperoleh begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style dengan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell open parentheses 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 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 end cell row blank equals cell g to the power of negative 1 end exponent open parentheses fraction numerator x plus 4 over denominator 2 x minus 3 end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses begin display style fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end style close parentheses minus 2 over denominator 3 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end style minus begin display style fraction numerator 2 open parentheses 2 x minus 3 close parentheses over denominator 2 x minus 3 end fraction end style over denominator 3 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x plus 4 minus 4 x plus 6 over denominator 2 x minus 3 end fraction end style over denominator 3 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 3 x plus 10 over denominator 2 x minus 3 end fraction end style over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 3 x plus 10 over denominator 2 x minus 3 end fraction cross times 1 third end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x plus 10 over denominator 6 x minus 9 end fraction end cell end table end style 

Jadi, dipeoleh begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 3 x plus 10 over denominator 6 x minus 9 end fraction end style.

0

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved