Roboguru

Jika , hitunglah .

Jika begin mathsize 14px style f open parentheses x close parentheses equals 1 half x plus 4 space dan space g open parentheses x close parentheses equals 3 x minus 7 end style, hitunglah begin mathsize 14px style 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 negative 2 close parentheses minus open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses negative 2 close parentheses end style

Jawaban:

begin mathsize 14px style f open parentheses x close parentheses equals 1 half x plus 4 space dan space g open parentheses x close parentheses equals 3 x minus 7 end style, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g open parentheses x close parentheses right parenthesis end cell row blank equals cell f left parenthesis 3 x minus 7 right parenthesis end cell row blank equals cell 1 half left parenthesis 3 x minus 7 right parenthesis plus 4 end cell row blank equals cell fraction numerator 3 x over denominator 2 end fraction minus 7 over 2 plus 4 end cell row blank equals cell fraction numerator 3 x minus 7 plus 8 over denominator 2 end fraction end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell row cell Jika space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 2 comma space maka space end cell row cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell equals cell negative 2 end cell row cell 3 x plus 1 end cell equals cell negative 4 end cell row cell 3 x end cell equals cell negative 5 end cell row x equals cell negative 5 over 3 end cell end table end style  

Jadi begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses equals negative 5 over 3 end style, berdasarkan sifat invers fungsi komposisi dapat ditulis begin mathsize 14px style 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 negative 2 close parentheses equals negative 5 over 3 end style.  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 1 half x plus 4 close parentheses end cell row blank equals cell 3 open parentheses 1 half x plus 4 close parentheses minus 7 end cell row blank equals cell 3 over 2 x plus 12 minus 7 end cell row blank equals cell 3 over 2 x plus 5 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 10 over denominator 2 end fraction end cell row cell Jika space open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell negative 2 comma space maka space end cell row cell fraction numerator 3 x plus 10 over denominator 2 end fraction end cell equals cell negative 2 end cell row cell 3 x plus 10 end cell equals cell negative 4 end cell row cell 3 x end cell equals cell negative 14 end cell row x equals cell negative 14 over 3 end cell end table end style 

Jadi begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses equals negative 14 over 3 end style, berdasarkan sifat invers fungsi komposisi maka dapat ditulis begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses negative 2 close parentheses equals negative 14 over 3 end style. Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis minus left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis end cell equals cell negative 5 over 3 minus open parentheses negative 14 over 3 close parentheses end cell row blank equals cell negative 5 over 3 plus 14 over 3 end cell row blank equals cell 9 over 3 end cell row blank equals 3 end table end style 

Jadi begin mathsize 14px style left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis minus left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis equals 3 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