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Jika dan , maka

Jika begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x minus 2 end fraction comma space x not equal to 2 over 3 end style dan begin mathsize 14px style f left parenthesis x right parenthesis equals x minus 2 end style, maka begin mathsize 14px style g left parenthesis 0 right parenthesis equals horizontal ellipsis end style 

  1. begin mathsize 14px style 4 end style 

  2. begin mathsize 14px style 3 end style 

  3. begin mathsize 14px style 4 over 3 end style 

  4. begin mathsize 14px style 1 end style 

  5. begin mathsize 14px style 3 over 4 end style 

Jawaban:

Diberikan fungsi invers dari komposisi begin mathsize 14px style g space dan space f end style, yaitu begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x minus 2 end fraction comma space x not equal to 2 over 3 end style.  Dimisalkan begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals y end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 2 x minus 1 over denominator 3 x minus 2 end fraction end cell row cell y left parenthesis 3 x minus 2 right parenthesis end cell equals cell 2 x minus 1 end cell row cell 3 y x minus 2 y end cell equals cell 2 x minus 1 end cell row cell 3 y x minus 2 x end cell equals cell 2 y minus 1 end cell row cell x left parenthesis 3 y minus 2 right parenthesis end cell equals cell 2 y minus 1 end cell row x equals cell fraction numerator 2 y minus 1 over denominator 3 y minus 2 end fraction end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis y right parenthesis end cell equals cell fraction numerator 2 y minus 1 over denominator 3 y minus 2 end fraction end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 1 over denominator 3 x minus 2 end fraction end cell end table end style  

Fungsi komposisi begin mathsize 14px style g space dan space f end style sama dengan fungsi inversnya. Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals x minus 2 end style, maka

 begin mathsize 14px style g left parenthesis x minus 2 right parenthesis equals fraction numerator 2 x minus 1 over denominator 3 x minus 2 end fraction end style 

Nilai begin mathsize 14px style g left parenthesis 0 right parenthesis end style didapatkan dengan mencari nilai begin mathsize 14px style x end style pada fungsi begin mathsize 14px style g left parenthesis x minus 2 right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals 0 row x equals 2 end table end style 

Dengan demikian, nilai begin mathsize 14px style g left parenthesis 0 right parenthesis end style yaitu

begin mathsize 14px style g left parenthesis 0 right parenthesis equals fraction numerator 2 times 2 minus 1 over denominator 3 times 2 minus 2 end fraction equals fraction numerator 4 minus 1 over denominator 6 minus 2 end fraction equals 3 over 4 end style.

Jadi, jawaban yang tepat adalah E.

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