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Diketahui fungsi begin mathsize 14px style f colon straight real numbers rightwards arrow straight real numbers end style dan begin mathsize 14px style g colon straight real numbers rightwards arrow straight real numbers end style dirumuskan dengan begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x minus 1 over denominator x end fraction end style, untuk begin mathsize 14px style x not equal to 0 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x plus 3 end style. Tentukanlah begin mathsize 14px style open parentheses g ring operator f open parentheses x close parentheses close parentheses to the power of negative 1 end exponent end style.

Jawaban:

Pada soal yang dimaksud tentukan begin mathsize 14px style open parentheses g open parentheses f open parentheses x close parentheses close parentheses close parentheses to the power of negative 1 end exponent equals open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style.

Permasalahan ini dapat diselesaikan dengan cara mencari fungsi komposisinya terlebih dahulu kemudian dicari fungsi invers dari fungsi kompisisi yang telah diperoleh.

Diketahui  begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x minus 1 over denominator x end fraction end style, untuk begin mathsize 14px style x not equal to 0 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x plus 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 left parenthesis x right parenthesis end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator x minus 1 over denominator x end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator x minus 1 over denominator x end fraction close parentheses plus 3 end cell row blank equals cell fraction numerator x minus 1 plus 3 x over denominator x end fraction end cell row blank equals cell fraction numerator 4 x minus 1 over denominator x end fraction comma x not equal to 0 end cell end table end style 

Diperoleh begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals fraction numerator 4 x minus 1 over denominator x end fraction end style kemudian dicari fungsi inversnya. Misalkan begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals y end style diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank left right double arrow cell y equals fraction numerator 4 x minus 1 over denominator x end fraction end cell row blank left right double arrow cell y x equals 4 x minus 1 end cell row blank left right double arrow cell x y minus 4 x equals negative 1 end cell row blank left right double arrow cell x equals fraction numerator negative 1 over denominator y minus 4 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator negative 1 over denominator y minus 4 end fraction comma y not equal to 4 end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 1 over denominator x minus 4 end fraction comma x not equal to 4 end cell end table end style  

Dengan demikian diperoleh Error converting from MathML to accessible text.

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