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Jika , maka  adalah ...

Pertanyaan

Jika f left parenthesis x right parenthesis equals fraction numerator x plus 2011 over denominator x minus 1 end fraction,

maka table attributes columnalign right center left columnspacing 0px end attributes row blank blank 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 end table 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  

Pembahasan Soal:

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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui fungsi  dan . Hasil dari  adalah ...

Pembahasan Soal:

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals square root of 2 x squared plus x plus 3 end root g open parentheses x close parentheses equals 4 x minus 2 end style 

Mencari fungsi komposisi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f left parenthesis 4 x minus 2 right parenthesis end cell row blank equals cell square root of 2 open parentheses 4 x minus 2 close parentheses squared plus 4 x minus 2 plus 3 end root end cell row blank equals cell square root of 2 open parentheses 16 x squared minus 16 x plus 4 close parentheses plus 4 x minus 2 plus 3 end root end cell row blank equals cell square root of 32 x squared minus 32 x plus 8 plus 4 x minus 2 plus 3 end root end cell row blank equals cell square root of 32 x squared minus 28 x plus 9 end root end cell end table end style 

Mencari begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell square root of 32 x squared minus 28 x plus 9 end root end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis end cell equals cell square root of 32 left parenthesis 2 right parenthesis squared minus 28 left parenthesis 2 right parenthesis plus 9 end root end cell row blank equals cell square root of 32 times 2 squared minus 28 open parentheses 2 close parentheses plus 9 end root end cell row blank equals cell square root of 2 squared times 32 minus 56 plus 9 end root end cell row blank equals cell square root of 2 squared times thin space 32 minus 47 end root end cell row blank equals cell square root of 128 minus 47 end root end cell row blank equals cell square root of 81 end cell row blank equals cell square root of 9 squared end root end cell row blank equals 9 end table end style 

Jadi, hasil dari begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis end style adalah 9.

0

Roboguru

Diketahui  dan . Tentukan: a.

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals 1 minus 3 x dan g left parenthesis x right parenthesis equals 2 x squared plus x, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 2 x squared plus x close parentheses end cell row blank equals cell 1 minus 3 open parentheses 2 x squared plus x close parentheses end cell row blank equals cell 1 minus 6 x squared minus 3 x end cell end table 

Jadi, open parentheses f ring operator g close parentheses open parentheses x close parentheses equals negative 6 x squared minus 3 x plus 1.

0

Roboguru

Diketahui fungsi  dan  dan . Tentukan

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f space ring operator space g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis end cell row blank equals cell f left parenthesis x plus 2 right parenthesis end cell row blank equals cell 3 left parenthesis x plus 2 right parenthesis plus 5 end cell row blank equals cell 3 x plus 6 plus 5 end cell row blank equals cell 3 x plus 11 end cell end table end style

Jadi hasil begin mathsize 14px style left parenthesis f space ring operator space g right parenthesis left parenthesis x right parenthesis end style adalah begin mathsize 14px style 3 x plus 11 end style.

0

Roboguru

Diketahui fungsi  dan . Komposisi fungsi ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g space ring operator space f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis 2 x minus 3 right parenthesis end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis squared plus 2 left parenthesis 2 x minus 3 right parenthesis minus 3 end cell row blank equals cell 4 x squared minus 12 x plus 9 plus 4 x minus 6 minus 3 end cell row blank equals cell 4 x squared minus 8 x end cell end table end style 

Sehingga, hasil komposisi fungsi begin mathsize 14px style left parenthesis g space ring operator space f right parenthesis left parenthesis x right parenthesis end style adalah Error converting from MathML to accessible text. 

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Jika diketahui  dan , komposisi fungsi dari  adalah ...

Pembahasan Soal:

Misalkan begin mathsize 14px style y equals x minus 3 end style maka begin mathsize 14px style x equals y plus 3 end style sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x minus 3 close parentheses end cell equals cell 6 x minus 11 end cell row cell f open parentheses y close parentheses end cell equals cell 6 open parentheses y plus 3 close parentheses minus 11 end cell row blank equals cell 6 y plus 18 minus 11 end cell row cell f open parentheses y close parentheses end cell equals cell 6 y plus 7 end cell row cell f open parentheses x close parentheses end cell equals cell 6 x plus 7 end cell end table end style 

Misalkan begin mathsize 14px style y equals x plus 1 end style maka begin mathsize 14px style x equals y minus 1 end style sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x plus 1 close parentheses end cell equals cell fraction numerator 2 x minus 6 over denominator 3 x plus 4 end fraction end cell row cell g open parentheses y close parentheses end cell equals cell fraction numerator 2 open parentheses y minus 1 close parentheses minus 6 over denominator 3 open parentheses y minus 1 close parentheses plus 4 end fraction end cell row blank equals cell fraction numerator 2 y minus 2 minus 6 over denominator 3 y minus 3 plus 4 end fraction end cell row cell g open parentheses y close parentheses end cell equals cell fraction numerator 2 y minus 8 over denominator 3 y plus 1 end fraction end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 2 x minus 8 over denominator 3 x plus 1 end fraction end cell end table end style  

Berdasarkan fungsi komposisi maka begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator 2 x minus 8 over denominator 3 x plus 1 end fraction close parentheses end cell row blank equals cell 6 open parentheses fraction numerator 2 x minus 8 over denominator 3 x plus 1 end fraction close parentheses plus 7 end cell row blank equals cell fraction numerator 12 x minus 48 over denominator 3 x plus 1 end fraction plus fraction numerator 7 open parentheses 3 x plus 1 close parentheses over denominator 3 x plus 1 end fraction end cell row blank equals cell fraction numerator 33 x minus 41 over denominator 3 x plus 1 end fraction end cell end table end style 

komposisi fungsi dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses 2 p plus 3 close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses 2 p plus 3 close parentheses end cell equals cell fraction numerator 33 open parentheses 2 p plus 3 close parentheses minus 41 over denominator 3 open parentheses 2 p plus 3 close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator 66 p plus 99 minus 41 over denominator 6 p plus 9 plus 1 end fraction end cell row blank equals cell fraction numerator 66 p plus 58 over denominator 6 p plus 10 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 33 p plus 29 close parentheses over denominator 2 open parentheses 3 p plus 5 close parentheses end fraction end cell row blank equals cell fraction numerator 33 p plus 29 over denominator 3 p plus 5 end fraction end cell end table end style 

Oleh karena itu, jawaban yang tepat adalah E.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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