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Diketahui , tentukan c.

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 space dan space g left parenthesis x right parenthesis equals x squared minus 7 end style, tentukan

c. size 14px left parenthesis size 14px f size 14px ring operator size 14px f size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis 

Pembahasan Video:

Pembahasan Soal:

Sesuai konsep left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis dan left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis, jika kita ubah g menjadi f agar dapat memenuhi left parenthesis f ring operator f right parenthesis left parenthesis x right parenthesis,

maka, left parenthesis f ring operator f right parenthesis left parenthesis x right parenthesis equals f left parenthesis f left parenthesis x right parenthesis right parenthesis

Lalu,

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

Dengan demikian, left parenthesis f ring operator f right parenthesis left parenthesis x right parenthesis equals 4 x plus 9

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Entry

Terakhir diupdate 12 Juli 2021

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Pertanyaan yang serupa

Fungsi-fungsi f dan g dinyatakan dalam pasangan terurut, tentukan  dan  dari fungsi f dan g berikut: a.  dan

Pembahasan Soal:

Fungsi f dan g dapat di komposisikan menjadi komposisi fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis end style bila undefined dan  dirumuskan oleh begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis end style 

Maka, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row cell g left parenthesis f left parenthesis negative 3 right parenthesis right parenthesis end cell equals cell g left parenthesis 1 right parenthesis equals negative 2 end cell row cell g left parenthesis f left parenthesis negative 2 right parenthesis right parenthesis end cell equals cell g left parenthesis 4 right parenthesis equals negative 3 end cell row cell g left parenthesis f left parenthesis negative 1 right parenthesis right parenthesis end cell equals cell g left parenthesis 5 right parenthesis equals 0 end cell row cell g left parenthesis f left parenthesis 0 right parenthesis right parenthesis end cell equals cell g left parenthesis 3 right parenthesis equals negative 1 end cell end table end style 

 Jadi, begin mathsize 14px style bold left parenthesis bold italic g bold ring operator bold italic f bold right parenthesis bold equals begin bold style left curly bracket left parenthesis negative 3 comma negative 2 right parenthesis comma space left parenthesis negative 2 comma negative 3 right parenthesis comma space left parenthesis negative 1 comma 0 right parenthesis comma space left parenthesis 0 comma negative 1 right parenthesis right curly bracket end style end style 

 

Fungsi f dan g dapat di komposisikan menjadi komposisi fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses end style bila begin mathsize 14px style R subscript g intersection D subscript f not equal to empty set end style dan  dirumuskan oleh 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 

Maka,

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 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell f left parenthesis g left parenthesis 4 right parenthesis right parenthesis end cell equals cell f left parenthesis negative 3 right parenthesis equals 1 end cell row cell f left parenthesis g left parenthesis 1 right parenthesis right parenthesis end cell equals cell f left parenthesis negative 2 right parenthesis equals 4 end cell row cell f left parenthesis g left parenthesis 3 right parenthesis right parenthesis end cell equals cell f left parenthesis negative 1 right parenthesis equals 5 end cell row cell f left parenthesis g left parenthesis 5 right parenthesis right parenthesis end cell equals cell f left parenthesis 0 right parenthesis equals 3 end cell end table end style 

Jadi,  begin mathsize 14px style begin bold style left parenthesis f ring operator g right parenthesis end style bold equals begin bold style left curly bracket left parenthesis 4 comma 1 right parenthesis comma space left parenthesis 1 comma 4 right parenthesis comma space left parenthesis 3 comma 5 right parenthesis comma space left parenthesis 5 comma 3 right parenthesis right curly bracket end style end style

Roboguru

Fungsi-fungsi  dan  berikut ini masing-masing adalah pemetaan dari . Tentukan rumus fungsi komposisi  dan . b.  dan

Pembahasan Soal:

Fungsi komposisi merupakan penggabungan operasi dua jenis fungsi atau lebih sehingga menghasilkan sebuah fungsi baru. Fungsi komposisi disimbolkan dengan begin mathsize 14px style " ring operator " end style (bundaran) Misalkan terdapat dua fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style  dan begin mathsize 14px style g open parentheses x close parentheses end style maka fungsi komposisi dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style.

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 1 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x plus 6 end style.

Dicari terlebih dahulu fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style 

   table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis begin mathsize 14px style left parenthesis x right parenthesis end style end cell equals cell begin mathsize 14px style f end style begin mathsize 14px style left parenthesis g open parentheses x close parentheses right parenthesis end style end cell row blank equals cell f begin mathsize 14px style left parenthesis 3 x plus 6 right parenthesis end style end cell row blank equals cell begin mathsize 14px style 2 end style begin mathsize 14px style open parentheses 3 x plus 6 close parentheses end style begin mathsize 14px style plus end style begin mathsize 14px style 1 end style end cell row blank equals cell begin mathsize 14px style 6 end style begin mathsize 14px style x end style begin mathsize 14px style plus end style begin mathsize 14px style 12 end style begin mathsize 14px style plus end style begin mathsize 14px style 1 end style end cell row blank equals cell begin mathsize 14px style 6 end style begin mathsize 14px style x end style begin mathsize 14px style plus end style begin mathsize 14px style 13 end style end cell end table

Dengan demikian diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g 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 equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 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 blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 13 end table end style.

Kemudian dicari fungsi komposisi begin mathsize 14px style open parentheses g ring operator f close parentheses 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 g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 2 x plus 1 close parentheses end cell row blank equals cell 3 open parentheses 2 x plus 1 close parentheses plus 6 end cell row blank equals cell 6 x plus 3 plus 6 end cell row blank equals cell 6 x plus 9 end cell end table end style  

Dengan demikian diperoleh begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 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 blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 9 end table end style

Roboguru

Diketahui fungsi  dan  dengan  dan . Tentukan  dan !

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell f open parentheses x squared minus 2 x plus 5 close parentheses end cell row blank equals cell 3 open parentheses x squared minus 2 x plus 5 close parentheses minus 2 end cell row blank equals cell 3 x squared minus 6 x plus 15 minus 2 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 3 x squared minus 6 x plus 13 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell g open parentheses 3 x minus 2 close parentheses end cell row blank equals cell left parenthesis 3 x minus 2 right parenthesis squared plus 2 left parenthesis 3 x minus 2 right parenthesis plus 5 end cell row blank equals cell 9 x squared minus 12 x plus 4 plus 6 x minus 4 plus 5 end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell 9 x squared minus 6 x plus 5 end cell end table end style 

Roboguru

Jika diketahui  dan   maka

Pembahasan Soal:

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses space space space space space space space space space space space space space space equals f open parentheses 5 x plus 16 close parentheses space space space space space space space space space space space space space space equals 3 open parentheses 5 x plus 16 close parentheses plus b space space space space space space space space space space space space space space equals 15 x plus 48 plus b open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses space space space space space space space space space space space space space space equals g open parentheses 3 x plus b close parentheses space space space space space space space space space space space space space space equals 5 open parentheses 3 x plus b close parentheses space space space space space space space space space space space space space space equals 15 x plus 5 b 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 left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell row cell up diagonal strike 15 x end strike plus 48 plus b end cell equals cell up diagonal strike 15 x end strike plus 5 b end cell row 48 equals cell 5 b minus b end cell row 48 equals cell 4 b end cell row b equals cell 48 over 4 end cell row b equals 12 row blank blank blank end table end style  

Jadi, jawaban yang tepat adalah B

 

Roboguru

Diketahui f(x) = 3x - 4 dan g(x) = 2x + p. Apabila f o g = g o f, maka nilai p adalah .....

Pembahasan Soal:

f left parenthesis x right parenthesis equals 3 x minus 4  g left parenthesis x right parenthesis equals 2 x plus p  f o g equals g o f  3 left parenthesis 2 x plus p right parenthesis minus 4 equals 2 left parenthesis 3 x minus 4 right parenthesis plus p  6 x plus 3 p minus 4 equals 6 x minus 8 plus p  2 p equals negative 4  p equals negative 2

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