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Jika P ( x ) = x + 1 x ​ dan R ( x ) = x − 1 x ​ , tentukan nilai ( R P ​ ) ( x )

Jika  dan , tentukan nilai 

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E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

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Jawaban

hasil dari adalah .

hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis P over R right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x minus 1 over denominator x plus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table end style.

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Pembahasan

Dengan menggunakan operasi pembagian dua fungsi diperoleh: Dengan demikian hasil dari adalah .

Dengan menggunakan operasi pembagian dua fungsi diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses P over R close parentheses open parentheses x close parentheses end cell equals cell fraction numerator P open parentheses x close parentheses over denominator R open parentheses x close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator x over denominator x plus 1 end fraction end style over denominator begin display style fraction numerator x over denominator x minus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator x over denominator x plus 1 end fraction times fraction numerator x minus 1 over denominator x end fraction end cell row blank equals cell fraction numerator x minus 1 over denominator x plus 1 end fraction space comma space x not equal to negative 1 end cell row blank blank blank end table end style

Dengan demikian hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis P over R right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x minus 1 over denominator x plus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table end style.

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