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Jika f ( x ) = x − 1 x + 2011 ​ , maka ​ ​ ( f ∘ f ∘ f ∘ f ∘ f ) ( x ) ​ adalah ...

Jika ,

maka  adalah ...

  1. fraction numerator x plus 2011 over denominator x minus 1 end fraction 

  2. fraction numerator x plus 2011 over denominator x plus 1 end fraction 

  3. fraction numerator x minus 2011 over denominator x plus 1 end fraction  

  4. fraction numerator x minus 2011 over denominator x minus 1 end fraction  

  5. fraction numerator negative x plus 2011 over denominator x minus 1 end fraction  

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

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Pembahasan

Diketahui . Ingat! Sehingga: Dari hasil perhitungan di atas, maka: Jadi, jawaban yang tepat adalah A.

Diketahui f left parenthesis x right parenthesis equals fraction numerator x plus 2011 over denominator x minus 1 end fraction.

Ingat!

  • f ring operator g equals f left parenthesis g left parenthesis x right parenthesis right parenthesis 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator f left parenthesis x right parenthesis end cell equals cell f left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell fraction numerator f left parenthesis x right parenthesis plus 2011 over denominator f left parenthesis x right parenthesis minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x plus 2011 over denominator x minus 1 end fraction end style plus 2011 over denominator begin display style fraction numerator x plus 2011 over denominator x minus 1 end fraction end style minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x plus 2011 over denominator x minus 1 end fraction end style plus begin display style fraction numerator 2011 x minus 2011 over denominator x minus 1 end fraction end style over denominator begin display style fraction numerator x plus 2011 over denominator x minus 1 end fraction end style minus begin display style fraction numerator x minus 1 over denominator x minus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x plus 2011 plus 2011 x minus 2011 over denominator x minus 1 end fraction end style over denominator begin display style fraction numerator x plus 2011 minus x plus 1 over denominator x minus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2012 x over denominator up diagonal strike x minus 1 end strike end fraction end style over denominator begin display style fraction numerator 2012 over denominator up diagonal strike x minus 1 end strike end fraction end style end fraction end cell row blank equals x end table 

Dari hasil perhitungan di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator f ring operator f ring operator f ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell left parenthesis f ring operator left parenthesis f ring operator f right parenthesis ring operator left parenthesis f ring operator f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell f left parenthesis x right parenthesis end cell row blank equals cell fraction numerator x plus 2011 over denominator x minus 1 end fraction end cell end table 

Jadi, jawaban yang tepat adalah A.

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