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Diketahui  dan . Jika  menyatakan invers dari , ma...

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x minus 2 over denominator x plus 2 end fraction end style dan begin mathsize 14px style g open parentheses x close parentheses equals x plus 2 end style. Jika begin mathsize 14px style f to the power of negative 1 end exponent end style menyatakan invers dari begin mathsize 14px style f end style, maka 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 space horizontal ellipsis end style 

  1. begin mathsize 14px style fraction numerator negative 4 x minus 4 over denominator x minus 1 end fraction semicolon space x not equal to 1 end style 

  2. begin mathsize 14px style fraction numerator negative 4 x over denominator x minus 1 end fraction semicolon space x not equal to 1 end style 

  3. begin mathsize 14px style fraction numerator 4 x over denominator x minus 1 end fraction semicolon space x not equal to 1 end style 

  4. begin mathsize 14px style fraction numerator 4 x plus 4 over denominator x minus 1 end fraction semicolon space x not equal to 1 end style 

  5. begin mathsize 14px style fraction numerator x over denominator x minus 4 end fraction semicolon space x not equal to 4 end style 

Jawaban:

Fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator open parentheses x plus 2 close parentheses minus 2 over denominator open parentheses x plus 2 close parentheses plus 2 end fraction end cell row blank equals cell fraction numerator x over denominator x plus 4 end fraction end cell end table end style

Invers dari fungsi komposisi tersebut adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator x over denominator x plus 4 end fraction end cell row y equals cell fraction numerator x over denominator x plus 4 end fraction end cell row cell x y plus 4 y end cell equals x row cell x y minus x end cell equals cell negative 4 y end cell row cell x open parentheses y minus 1 close parentheses end cell equals cell negative 4 y end cell row x equals cell fraction numerator negative 4 y over denominator y minus 1 end fraction 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 4 x over denominator x minus 1 end fraction end cell end table end style

Oleh karena itu, jawaban yang tepat adalah B.

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