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

Pertanyaan

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 begin mathsize 14px style 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 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 ?  

   space undefined

Pembahasan:

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 

Jawaban terverifikasi

Dijawab oleh:

M. Alfi

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 06 Oktober 2021

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Diketahui  dan   b.  (g−1∘f−1)(x)?

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