Roboguru

Jika , hitunglah .

Jika begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 5 space dan space g open parentheses x close parentheses equals fraction numerator x minus 2 over denominator 2 x plus 3 end fraction comma space x not equal to negative 3 over 2 end style, hitunglah begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 6 close parentheses plus open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 1 close parentheses end style

Jawaban:

Menentukan invers fungsi begin mathsize 14px style f open parentheses x close parentheses end style

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 plus 5 end cell row y equals cell 3 x plus 5 end cell row cell 3 x end cell equals cell y minus 5 end cell row x equals cell fraction numerator y minus 5 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 minus 5 over denominator 3 end fraction end cell end table end style 

Menentukan invers fungsi begin mathsize 14px style g open parentheses x close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator 2 x plus 3 end fraction end cell row y equals cell fraction numerator x minus 2 over denominator 2 x plus 3 end fraction end cell row cell y open parentheses 2 x plus 3 close parentheses end cell equals cell x minus 2 end cell row cell 2 x y plus 3 y end cell equals cell x minus 2 end cell row cell 2 x y minus x end cell equals cell negative 3 y minus 2 end cell row cell x open parentheses 2 y minus 1 close parentheses end cell equals cell negative 3 y minus 2 end cell row x equals cell fraction numerator negative 3 y minus 2 over denominator 2 y minus 1 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 negative 3 x minus 2 over denominator 2 x minus 1 end fraction end cell end table end style 

Menentukan begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 6 close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 6 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 6 close parentheses end cell row blank blank blank row cell f to the power of negative 1 end exponent open parentheses 6 close parentheses end cell equals cell fraction numerator 6 minus 5 over denominator 3 end fraction end cell row blank equals cell 1 third end cell row blank blank blank row 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 6 close parentheses end cell equals cell g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses 6 close parentheses close parentheses end cell row blank equals cell g to the power of negative 1 end exponent open parentheses 1 third close parentheses end cell row blank equals cell fraction numerator negative 3 open parentheses begin display style 1 third end style close parentheses minus 2 over denominator 2 open parentheses begin display style 1 third end style close parentheses minus 1 end fraction end cell row blank equals cell fraction numerator negative 1 minus 2 over denominator begin display style 2 over 3 end style minus 3 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator negative begin display style 7 over 3 end style end fraction end cell row blank equals cell 9 over 7 end cell end table end style  

menentukan begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 1 close parentheses 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 to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell equals cell 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 1 close parentheses end cell row blank blank blank row cell g to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell equals cell fraction numerator negative 3 open parentheses negative 1 close parentheses minus 2 over denominator 2 open parentheses negative 1 close parentheses minus 1 end fraction end cell row blank equals cell negative 1 third end cell row blank blank blank row cell 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 1 close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses negative 1 close parentheses close parentheses end cell row blank equals cell f to the power of negative 1 end exponent open parentheses negative 1 third close parentheses end cell row blank equals cell fraction numerator negative begin display style 1 third end style minus 5 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative begin display style 16 over 3 end style over denominator 3 end fraction end cell row blank equals cell negative 16 over 9 end cell end table 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 to the power of negative 1 end exponent left parenthesis 6 right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis end cell equals cell fraction numerator 9 over denominator 7 end fraction plus open parentheses negative 19 over 9 close parentheses end cell row blank equals cell 9 over 7 minus 19 over 9 end cell row blank equals cell fraction numerator 81 minus 133 over denominator 63 end fraction end cell row blank equals cell negative 52 over 63 end cell end table end style  

Jadi begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 6 right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals negative 52 over 63 end style.

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