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Diketahui  dan . Tentukan :

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 5 x minus 1 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x plus 3 end style. Tentukan :

begin mathsize 14px style open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis end style  

Jawaban:

Dari soal tersebut diketahui dan didapat sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 5 x minus 1 end cell row a equals cell 5 x minus 1 end cell row cell 5 x end cell equals cell a plus 1 end cell row x equals cell fraction numerator a plus 1 over denominator 5 end fraction end cell end table end style 

Berarti, begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator 5 end fraction end style.

Berikutnya,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell x plus 3 end cell row b equals cell x plus 3 end cell row x equals cell b minus 3 end cell end table end style 

Berarti, begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis equals x minus 3 end style 

Dari kedua hal tersebut, maka dapat dihitung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes 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 left parenthesis x right parenthesis end cell equals cell g to the power of negative 1 end exponent left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell open parentheses f to the power of negative 1 end exponent left parenthesis x right parenthesis close parentheses minus 3 end cell row blank equals cell open parentheses fraction numerator x plus 1 over denominator 5 end fraction close parentheses minus 3 end cell row blank equals cell fraction numerator x plus 1 over denominator 5 end fraction minus 15 over 5 end cell row blank equals cell fraction numerator x plus 1 minus 15 over denominator 5 end fraction end cell row blank equals cell fraction numerator x minus 14 over denominator 5 end fraction end cell end table end style 

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