Roboguru

Diketahui fungsi  f(x)=2x−3 dan fungsi g(x)=x2−4x−5. Tentukan fungsi komposisi (f∘g)(x)!

Pertanyaan

Diketahui fungsi  f left parenthesis x right parenthesis equals 2 x minus 3 dan fungsi g left parenthesis x right parenthesis equals x squared minus 4 x minus 5. Tentukan fungsi komposisi left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis!

Pembahasan Soal:

Dengan menggunakan konsep komposisi dua fungsi diperoleh:

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 2 left parenthesis x squared minus 4 x minus 5 right parenthesis minus 3 end cell row blank equals cell 2 x squared minus 8 x minus 10 minus 3 end cell row blank equals cell 2 x squared minus 8 x minus 13 end cell end table

Jadi,

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 2 x squared minus 8 x minus 13 end cell end table

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Putri

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Fungsi f dan g adalah pemetaan dari R ke R yang dirumuskan oleh f(x)=3x+2dan (x)=x+3.  maka nilai (gof)(−1) adalah ...

Pembahasan Soal:

Diasumsikan left parenthesis x right parenthesis equals x plus 3 adalah fungsi g left parenthesis x right parenthesis equals x plus 3 

Sehingga dari soal diketahui

f open parentheses x close parentheses equals 3 x plus 2 g open parentheses x close parentheses equals x plus 3      

 Fungsi left parenthesis g o f right parenthesis left parenthesis x right parenthesis dapat ditentukan dengan cara berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 3 x plus 2 close parentheses end cell row blank equals cell 3 x plus 2 plus 3 end cell row blank equals cell 3 x plus 5 end cell end table 

Nilai left parenthesis g o f right parenthesis left parenthesis negative 1 right parenthesis adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses negative 1 close parentheses end cell equals cell 3 open parentheses negative 1 close parentheses plus 5 end cell row blank equals cell negative 3 plus 5 end cell row blank equals 2 end table 

Jadi, Nilai dari left parenthesis g o f right parenthesis left parenthesis negative 1 right parenthesis adalah 2 

 

 

 

0

Roboguru

Diberikan f(x)=x2+2 dan g(x)=x2−2. Hasil dari (g∘f)(x)−(f∘g)(x)=....

Pembahasan Soal:

Diberikan  dan .

Dit :  

Kita cari masing2 komposisi fungsinya.

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals g open parentheses f left parenthesis x right parenthesis close parentheses end style

               begin mathsize 14px style equals g open parentheses x squared plus 2 close parentheses equals open parentheses x squared plus 2 close parentheses squared minus 2 equals x to the power of 4 plus 4 x squared plus 4 minus 2 equals x to the power of 4 plus 4 x squared plus 2 end style

begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis end style

              begin mathsize 14px style equals f left parenthesis g left parenthesis x right parenthesis right parenthesis equals f left parenthesis x squared minus 2 right parenthesis equals left parenthesis x squared minus 2 right parenthesis squared plus 2 equals x to the power of 4 minus 4 x squared plus 4 plus 2 equals x to the power of 4 minus 4 x squared plus 6 end style

maka :

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis minus left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis x to the power of 4 plus 4 x squared plus 2 right parenthesis minus open parentheses x to the power of 4 minus 4 x squared plus 6 close parentheses equals 8 x squared minus 4 end style

jadi, jawabannya  

0

Roboguru

Diketahui fungsi f:R→R dan g:R→R dengan g(x)=4x+3 dan (f∘g)(x)=8x−1, maka nilai f(4) adalah ....

Pembahasan Soal:

Menentukan f left parenthesis x right parenthesis

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 8 x minus 1 end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 8 x minus 1 end cell row cell f left parenthesis 4 x plus 3 right parenthesis end cell equals cell 8 x minus 1 end cell end table

Misalkan

table attributes columnalign right center left columnspacing 0px end attributes row t equals cell 4 x plus 3 end cell row cell 4 x end cell equals cell t minus 3 end cell row x equals cell fraction numerator t minus 3 over denominator 4 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis t right parenthesis end cell equals cell 8 open parentheses fraction numerator t minus 3 over denominator 4 end fraction close parentheses minus 1 end cell row cell f left parenthesis t right parenthesis end cell equals cell 2 t minus 6 minus 1 end cell row cell f left parenthesis x right parenthesis end cell equals cell 2 x minus 7 end cell end table

 

Menentukan f left parenthesis 4 right parenthesis

table row cell f open parentheses 4 close parentheses equals 2 open parentheses 4 close parentheses minus 7 end cell row cell f open parentheses 4 close parentheses equals 8 minus 1 end cell row cell f open parentheses 4 close parentheses equals 1 end cell end table 

Oleh karena itu, jawaban yang benar adalah C.

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Roboguru

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

Pembahasan Soal:

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.
 

0

Roboguru

Diketahuifungsif(x)=x2+4x+1dang(x)=2x+1.Fungsikomposisi(fog)(x)=...

Pembahasan Soal:

f left parenthesis x right parenthesis equals x squared plus 4 x plus 1  g left parenthesis x right parenthesis space equals space 2 x plus 1  m a k a  left parenthesis f o g right parenthesis space left parenthesis x right parenthesis space equals space f left parenthesis g left parenthesis x right parenthesis right parenthesis  equals f left parenthesis 2 x plus 1 right parenthesis  equals left parenthesis 2 x plus 1 right parenthesis squared plus 4 left parenthesis 2 x plus 1 right parenthesis plus 1  equals left parenthesis 4 x squared plus 4 x plus 1 right parenthesis plus 8 x plus 4 plus 1  equals 4 x squared plus 12 x plus 6

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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