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Jika diketahui f(x−3)=6x−11 dan g(x+1)=3x−42x−6​, komposisi fungsi dari (f∘g)(2p+3) adalah ....

Pertanyaan

Jika diketahui begin mathsize 14px style f left parenthesis x minus 3 right parenthesis equals 6 x minus 11 end style dan begin mathsize 14px style g left parenthesis x plus 1 right parenthesis equals fraction numerator 2 x minus 6 over denominator 3 x minus 4 end fraction end style, komposisi fungsi dari begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis 2 p plus 3 right parenthesis end style adalah ....

  1. begin mathsize 14px style fraction numerator 33 p plus 39 over denominator 3 p plus 5 end fraction end style 

  2. begin mathsize 14px style fraction numerator 33 p minus 29 over denominator 3 p plus 4 end fraction end style 

  3. begin mathsize 14px style fraction numerator 33 p plus 29 over denominator 3 p minus 5 end fraction end style 

  4. begin mathsize 14px style fraction numerator 33 p plus 34 over denominator 3 p plus 4 end fraction end style 

  5. begin mathsize 14px style fraction numerator 33 p plus 29 over denominator 3 p plus 5 end fraction end style 

Pembahasan:

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis 2 p plus 3 right parenthesis equals f left parenthesis g left parenthesis 2 p plus 3 right parenthesis right parenthesis end style
 

Akan dicari hasil dari begin mathsize 14px style g left parenthesis 2 p plus 3 right parenthesis end style terlebih dahulu.

Diketahui begin mathsize 14px style g left parenthesis x plus 1 right parenthesis equals fraction numerator 2 x minus 6 over denominator 3 x plus 4 end fraction end style, akan dicari nilai begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style 2 p plus 3 end style
 

begin mathsize 14px style g left parenthesis x plus 1 right parenthesis rightwards double arrow g left parenthesis 2 p plus 3 right parenthesis x plus 1 equals 2 p plus 3 x equals 2 p plus 2 end style
 

didapat nilai begin mathsize 14px style x equals 2 p plus 2 end style, maka
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x plus 1 right parenthesis end cell equals cell fraction numerator 2 x minus 6 over denominator 3 x plus 4 end fraction end cell row cell g left parenthesis open parentheses 2 p plus 2 close parentheses plus 1 right parenthesis end cell equals cell fraction numerator 2 left parenthesis 2 p plus 2 right parenthesis minus 6 over denominator 3 left parenthesis 2 p plus 2 right parenthesis plus 4 end fraction end cell row cell g left parenthesis 2 p plus 3 right parenthesis end cell equals cell fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction end cell end table end style
 

didapat begin mathsize 14px style g left parenthesis 2 p plus 3 right parenthesis equals fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction end style, subtitusikan ke undefined
 

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 2 p plus 3 right parenthesis end cell equals cell f left parenthesis g left parenthesis 2 p plus 3 right parenthesis right parenthesis end cell row blank equals cell f open parentheses fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction close parentheses end cell end table end style
 

Diketahui begin mathsize 14px style f left parenthesis x minus 3 right parenthesis equals 6 x minus 11 end style, akan dicari nilai undefined yang memenuhi begin mathsize 14px style f open parentheses fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction close parentheses end style.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 3 end cell equals cell fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction end cell row x equals cell fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction plus 3 end cell row blank equals cell fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction plus fraction numerator 3 left parenthesis 6 p plus 10 right parenthesis over denominator 6 p plus 10 end fraction end cell row blank equals cell fraction numerator 4 p minus 2 plus 18 p plus 30 over denominator 6 p plus 10 end fraction end cell row blank equals cell fraction numerator 22 p plus 28 over denominator 6 p plus 10 end fraction end cell end table end style
 

Didapat begin mathsize 14px style x equals fraction numerator 22 p plus 28 over denominator 6 p plus 10 end fraction end style, subtitusikan undefined ke undefined.
 

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x minus 3 right parenthesis end cell equals cell 6 x minus 11 end cell row cell f open parentheses fraction numerator 22 p plus 28 over denominator 6 p plus 10 end fraction minus 3 close parentheses end cell equals cell 6 open parentheses fraction numerator 22 p plus 28 over denominator 6 p plus 10 end fraction close parentheses minus 11 end cell row cell f open parentheses fraction numerator 4 p minus 2 over denominator 6 p plus 10 end fraction close parentheses end cell equals cell fraction numerator 132 p plus 168 over denominator 6 p plus 10 end fraction minus fraction numerator 11 left parenthesis 6 p plus 10 right parenthesis over denominator 6 p plus 10 end fraction end cell row blank equals cell fraction numerator 132 p plus 168 minus 66 p minus 110 over denominator 6 p plus 10 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 33 p plus 29 over denominator 3 p plus 5 end fraction end cell end table end style
 

Didapat komposisi fungsi 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 2 p plus 3 right parenthesis end cell 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 benar adalah E.
 

Jawaban terverifikasi

Dijawab oleh:

I. Ridha

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 05 Oktober 2021

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