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Diketahui dan c. Apakah ( f − 1 ∘ g − 1 ) ( x ) = ( g − 1 ∘ f − 1 ) ( x ) ?

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals x minus 3 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 2 x plus 4 end style 

c. Apakah  ?  

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Jawaban terverifikasi

Jawaban

diperoleh bahwa

diperoleh bahwa open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses not equal to left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis               undefined 

Pembahasan

Dengan menggunakan rumus invers fungsi Diperoleh Nilai adalah dimasukkan ke Nilai adalah dimasukkan ke Diperoleh bahwa Jadi, diperoleh bahwa

Dengan menggunakan rumus invers fungsi

begin mathsize 14px style z open parentheses x close parentheses equals a x plus b blank semicolon a not equal to 0 z to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus b over denominator a end fraction blank semicolon a not equal to 0 end style 

Diperoleh 

begin mathsize 14px style f open parentheses x close parentheses equals x minus 3 f to the power of negative 1 end exponent open parentheses x close parentheses equals x plus 3 g open parentheses x close parentheses equals 2 x plus 4 g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 4 over denominator 2 end fraction end style 

Nilai undefined adalah begin mathsize 14px style g to the power of negative 1 end exponent end style dimasukkan ke begin mathsize 14px style f to the power of negative 1 end exponent space colon space left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end style 

begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator x minus 4 over denominator 2 end fraction plus 3 open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator x minus 4 over denominator 2 end fraction plus 6 over 2 open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator x plus 2 over denominator 2 end fraction  end style 

Nilai begin mathsize 14px style left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end style adalah begin mathsize 14px style f to the power of negative 1 end exponent end style dimasukkan ke begin mathsize 14px style g to the power of negative 1 end exponent space colon space left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals 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 style 

begin mathsize 14px style left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals fraction numerator left parenthesis x plus 3 right parenthesis minus 4 over denominator 2 end fraction left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals fraction numerator x minus 1 over denominator 2 end fraction end style 

Diperoleh bahwa 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row cell fraction numerator x plus 2 over denominator 2 end fraction end cell not equal to cell fraction numerator x minus 1 over denominator 2 end fraction end cell row blank blank blank end table end style 

Jadi, diperoleh bahwa open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses not equal to left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis               undefined 

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