Roboguru

Diketahui  dan , maka tentukan !

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 5 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x minus 1 over denominator x plus 4 end fraction end style, maka tentukan begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis 5 right parenthesis end style!

Jawaban:

Diketahui hal-hal sebagai berikut:

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Sehingga fungsi komposisi yang terbentuk adalah memenuhi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 2 open parentheses fraction numerator x minus 1 over denominator x plus 4 end fraction close parentheses plus 5 end cell row blank equals cell fraction numerator 2 x minus 2 over denominator x plus 4 end fraction plus 5 end cell row blank equals cell fraction numerator left parenthesis 2 x minus 2 right parenthesis plus left parenthesis 5 x plus 20 right parenthesis over denominator x plus 4 end fraction end cell row blank equals cell fraction numerator 7 x plus 18 over denominator x plus 4 end fraction end cell end table end style  

Untuk mencari invers tersebut maka dilakukan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell row y equals cell fraction numerator 7 x plus 18 over denominator x plus 4 end fraction end cell row cell y left parenthesis x plus 4 right parenthesis end cell equals cell 7 x plus 18 end cell row cell y x plus 4 y end cell equals cell 7 x plus 18 end cell row cell y x minus 7 x end cell equals cell 18 minus 4 y end cell row cell x left parenthesis y minus 7 right parenthesis end cell equals cell 18 minus 4 y end cell row x equals cell fraction numerator 18 minus 4 y over denominator y minus 7 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 18 minus 4 x over denominator x minus 7 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis 5 right parenthesis end cell equals cell fraction numerator 18 minus 4 times 5 over denominator 5 minus 7 end fraction end cell row blank equals cell fraction numerator negative 2 over denominator negative 2 end fraction end cell row blank equals 1 end table end style   

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