Pertanyaan

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

Jika $f (x) = \frac{x + 2011}{x - 1}$ ,

maka $(f \circ f \circ f \circ f \circ f) (x)$ adalah ...

$fraction numerator x plus 2011 over denominator x minus 1 end fraction$
$fraction numerator x plus 2011 over denominator x plus 1 end fraction$
$fraction numerator x minus 2011 over denominator x plus 1 end fraction$
$fraction numerator x minus 2011 over denominator x minus 1 end fraction$
$fraction numerator negative x plus 2011 over denominator x minus 1 end fraction$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

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!

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.