Roboguru

Difetahui  dan . Komposisi

Pertanyaan

Difetahui f equals open curly brackets left parenthesis 4 comma 4 right parenthesis comma left parenthesis 5 comma 6 right parenthesis comma left parenthesis 6 comma 8 right parenthesis comma left parenthesis 8 comma 10 right parenthesis close curly brackets dan g equals open curly brackets left parenthesis 4 comma 6 right parenthesis comma left parenthesis 6 comma 8 right parenthesis comma left parenthesis 2 comma 10 right parenthesis close curly brackets. Komposisi open parentheses f ring operator g close parentheses equals horizontal ellipsis 

  1. open curly brackets left parenthesis 4 comma 0 right parenthesis comma space left parenthesis 6 comma 8 right parenthesis close curly brackets 

  2. open curly brackets left parenthesis 4 comma 8 right parenthesis comma space left parenthesis 6 comma 10 right parenthesis close curly brackets 

  3. open curly brackets left parenthesis 4 comma 6 right parenthesis comma space left parenthesis 6 comma 10 right parenthesis close curly brackets 

  4. open curly brackets left parenthesis 4 comma 8 right parenthesis comma space left parenthesis 6 comma 10 right parenthesis comma space left parenthesis 10 comma 7 right parenthesis close curly brackets 

  5. open curly brackets left parenthesis 4 comma 0 right parenthesis comma space left parenthesis 6 comma 10 right parenthesis comma space left parenthesis 10 comma 12 right parenthesis close curly brackets 

Pembahasan Soal:

Diberikan fungsi f equals open curly brackets left parenthesis 4 comma 4 right parenthesis comma left parenthesis 5 comma 6 right parenthesis comma left parenthesis 6 comma 8 right parenthesis comma left parenthesis 8 comma 10 right parenthesis close curly brackets dan g equals open curly brackets left parenthesis 4 comma 6 right parenthesis comma left parenthesis 6 comma 8 right parenthesis comma left parenthesis 2 comma 10 right parenthesis close curly brackets. Komposisi dari dua fungsi tersebut dapat dikerjakan dengan terlebih dahulu mensubstitusikan domain fungsi g seperti berikut :

x equals 4 rightwards arrow open parentheses f ring operator g close parentheses left parenthesis 4 right parenthesis equals f left parenthesis g left parenthesis 4 right parenthesis right parenthesis equals f left parenthesis 6 right parenthesis equals 8 x equals 6 rightwards arrow open parentheses f ring operator g close parentheses left parenthesis 6 right parenthesis equals f left parenthesis g left parenthesis 6 right parenthesis right parenthesis equals f left parenthesis 8 right parenthesis equals 10 x equals 2 rightwards arrow left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis equals f left parenthesis g left parenthesis 2 right parenthesis right parenthesis equals f left parenthesis 10 right parenthesis equals negative

Dengan demikian, himpunan fungsi komposisi left parenthesis f ring operator g right parenthesis adalah open curly brackets left parenthesis 4 comma 8 right parenthesis comma space left parenthesis 6 comma 10 right parenthesis close curly brackets.

Jadi, jawaban yang terbentuk adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan . Invers fungsi  adalah

Pembahasan Soal:

Diketahui :

begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 5 x minus 3 over denominator x plus 2 end fraction comma space x not equal to 2 end style 
begin mathsize 14px style g left parenthesis x right parenthesis equals 6 x minus 2 end style

Ditanya :

Invers fungsi begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style 

Jawab :

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis f left parenthesis g left parenthesis x right parenthesis right parenthesis left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis f left parenthesis 6 x minus 2 right parenthesis right parenthesis left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 left parenthesis 6 x minus 2 right parenthesis minus 3 over denominator left parenthesis 6 x minus 2 right parenthesis plus 2 end fraction left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 30 x minus 10 minus 3 over denominator 6 x minus 2 plus 2 end fraction left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 30 x minus 13 over denominator 6 x end fraction end style 

invers fungsi sebagai berikut :

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 30 x minus 13 over denominator 6 x end fraction y equals fraction numerator 30 x minus 13 over denominator 6 x end fraction y left parenthesis 6 x right parenthesis equals 30 x minus 13 6 x y minus 30 x equals negative 13 x left parenthesis 6 y minus 30 right parenthesis equals negative 13 x equals fraction numerator negative 13 over denominator 6 y minus 30 end fraction left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 13 over denominator 6 x minus 30 end fraction comma space x not equal to 5 end style   

 

0

Roboguru

Diketahui fungsi  dan . Hasil dari  adalah ...

Pembahasan Soal:

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x squared minus 5 x plus 6 end cell row cell g open parentheses x close parentheses end cell equals cell x minus 2 end cell end table end style 

Mencari begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x 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 f left parenthesis g open parentheses x close parentheses right parenthesis end cell row blank equals cell f left parenthesis x minus 2 right parenthesis end cell row blank equals cell 2 open parentheses x minus 2 close parentheses squared minus 5 open parentheses x minus 2 close parentheses plus 6 end cell row blank equals cell 2 open parentheses x squared minus 4 x plus 4 close parentheses minus 5 x plus 10 plus 6 end cell row blank equals cell 2 x squared minus 8 x plus 8 minus 5 x plus 10 plus 6 end cell row blank equals cell 2 x squared minus 13 x plus 24 end cell end table end style 

Jadi, hasil dari begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style adalah begin mathsize 14px style 2 x squared minus 13 x plus 24 end style.

0

Roboguru

Diketahui fungsi  dan . Hasil dari  adalah... .

Pembahasan Soal:

Diketahui fungsi f open parentheses x close parentheses equals 2 x squared minus 5 x plus 6 dan g open parentheses x close parentheses equals x minus 2. Fungsi komposisi open parentheses f ring operator g close parentheses open parentheses x close parentheses sebagai berikut.

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 x minus 2 close parentheses end cell row blank equals cell 2 open parentheses x minus 2 close parentheses squared minus 5 open parentheses x minus 2 close parentheses plus 6 end cell row blank equals cell 2 open parentheses x squared minus 4 x plus 4 close parentheses minus 5 x plus 10 plus 6 end cell row blank equals cell 2 x squared minus 8 x plus 8 minus 5 x plus 16 end cell row blank equals cell 2 x squared minus 13 x plus 24 end cell end table


Dengan demikian, hasil dari open parentheses f ring operator g close parentheses open parentheses x close parentheses adalah open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x squared minus 13 x plus 24.

0

Roboguru

Diketahui fungsi  dan . Hasil dari  adalah ...

Pembahasan Soal:

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 2 left parenthesis x minus 2 right parenthesis squared minus 5 left parenthesis x minus 2 right parenthesis plus 6 end cell row blank equals cell 2 left parenthesis x squared minus 4 x plus 4 right parenthesis minus 5 x minus 10 plus 6 end cell row blank equals cell 2 x squared minus 8 x plus 8 minus 5 x minus 4 end cell row blank equals cell 2 x squared minus 13 x plus 4 end cell end table end style

0

Roboguru

Pembahasan Soal:

f left parenthesis x right parenthesis equals negative x plus 3  f left parenthesis x squared right parenthesis equals negative x squared plus 3  left parenthesis f left parenthesis x right parenthesis right parenthesis squared equals left parenthesis negative x plus 3 right parenthesis squared equals x squared minus 6 x plus 9  f left parenthesis x squared right parenthesis plus left square bracket f left parenthesis x squared right parenthesis right square bracket squared minus 2 f left parenthesis x right parenthesis  equals negative x squared plus 3 plus x squared minus 6 x plus 9 minus 2 left parenthesis negative x plus 3 right parenthesis  equals negative 4 x plus 6

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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