Roboguru

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

Pertanyaan

Fungsi-fungsi f dan g dinyatakan dalam pasangan terurut, tentukan begin mathsize 14px style open parentheses g ring operator f close parentheses end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses end style dari fungsi f dan g berikut:

c. begin mathsize 14px style f equals open curly brackets left parenthesis negative 1 comma 3 right parenthesis comma space left parenthesis 0 comma negative 1 right parenthesis comma space left parenthesis 1 comma 2 right parenthesis comma space left parenthesis 4 comma 7 right parenthesis close curly brackets end style dan begin mathsize 14px style g equals open curly brackets left parenthesis 2 comma 1 right parenthesis comma space left parenthesis 3 comma 4 right parenthesis comma space left parenthesis 6 comma negative 1 right parenthesis comma space left parenthesis 7 comma 0 right parenthesis close curly brackets end style 

Pembahasan Soal:

Fungsi f dan g dapat di komposisikan menjadi komposisi fungsi undefined bila begin mathsize 14px style R subscript f intersection D subscript g not equal to empty set end style 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 1 right parenthesis right parenthesis end cell equals cell g left parenthesis 3 right parenthesis equals 4 end cell row cell g left parenthesis f left parenthesis 0 right parenthesis right parenthesis end cell equals cell g left parenthesis negative 1 right parenthesis equals tidak space ada end cell row cell g left parenthesis f left parenthesis 1 right parenthesis right parenthesis end cell equals cell g left parenthesis 2 right parenthesis equals 1 end cell row cell g left parenthesis f left parenthesis 4 right parenthesis right parenthesis end cell equals cell g left parenthesis 7 right parenthesis equals 0 end cell row blank blank blank 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 bold left curly bracket bold left parenthesis bold minus bold 1 bold comma bold 4 bold right parenthesis bold comma bold space bold left parenthesis bold 1 bold comma bold 1 bold right parenthesis bold comma bold space bold left parenthesis bold 4 bold comma bold 0 bold right parenthesis bold right curly bracket end style   

 

Fungsi f dan g dapat di komposisikan menjadi komposisi fungsi undefined 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 left parenthesis x right parenthesis 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 2 right parenthesis right parenthesis end cell equals cell f left parenthesis 1 right parenthesis equals 2 end cell row cell f left parenthesis g left parenthesis 3 right parenthesis right parenthesis end cell equals cell f left parenthesis 4 right parenthesis equals 7 end cell row cell f left parenthesis g left parenthesis 6 right parenthesis right parenthesis end cell equals cell f left parenthesis negative 1 right parenthesis equals 3 end cell row cell f left parenthesis g left parenthesis 7 right parenthesis right parenthesis end cell equals cell f left parenthesis 0 right parenthesis equals negative 1 end cell end table end style 

Jadi,  begin mathsize 14px style bold left parenthesis bold italic f bold ring operator bold italic g bold right parenthesis bold equals bold left curly bracket bold left parenthesis bold 2 bold comma bold 2 bold right parenthesis bold comma bold space bold left parenthesis bold 3 bold comma bold 7 bold right parenthesis bold comma bold space bold left parenthesis bold 6 bold comma bold 3 bold right parenthesis bold comma bold space bold left parenthesis bold 7 bold comma bold minus bold 1 bold right parenthesis bold right curly bracket end style   

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFREELANCETIGASATU

Terakhir diupdate 30 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Diketahui  dan . Rumus

Pembahasan Soal:

Diketahui  dan . Rumus  

kita sederhanakan dulu fungsinya,

 = begin mathsize 14px style open parentheses x plus 2 close parentheses squared end style 

 = begin mathsize 14px style open parentheses x minus 2 close parentheses squared end style 

kemudian tentukan dulu fungsi komposisinya:

size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 4 plus 2 right parenthesis end style to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis end style to the power of size 14px 2 size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px g size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared plus 4 x plus 4 minus 2 right parenthesis end style to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space  square root of size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px plus square root of size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px equals square root of begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis squared end style end root size 14px plus square root of size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 end root size 14px equals size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 size 14px plus size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px equals size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 8

jadi, jawabannya C

 

 

0

Roboguru

Jika f(x) =  dan , fungsi

Pembahasan Soal:

Jika f(x) =  dan , fungsi  

kita cari komposisi fungsinya dulu,

begin mathsize 14px style 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 equals f left parenthesis x plus 2 right parenthesis equals left parenthesis x plus 2 right parenthesis minus 2 equals x 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 equals g left parenthesis x minus 2 right parenthesis equals left parenthesis x minus 2 right parenthesis plus 2 equals x left curly bracket left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis right curly bracket times left curly bracket left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis right curly bracket equals x times x equals x squared end style

jadi, jawabannya C

0

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

0

Roboguru

Diketahui . Jika  dan , maka nilai

Pembahasan Soal:

Jika diketahui g open parentheses f open parentheses x close parentheses close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses, maka nilai a dapat ditentukan sebagai berikut.

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 f open parentheses g open parentheses x close parentheses close parentheses end cell row cell 2 times f open parentheses x close parentheses plus 70 end cell equals cell 3 times g open parentheses x close parentheses plus a end cell row cell 2 open parentheses 3 x plus a close parentheses plus 70 end cell equals cell 3 open parentheses 2 x plus 70 close parentheses plus a end cell row cell 6 x plus 2 a plus 70 end cell equals cell 6 x plus 210 plus a end cell row cell 2 a minus a end cell equals cell 210 minus 70 end cell row a equals 140 end table

Dengan demikian, nilai a equals 140 

0

Roboguru

Fungsi-fungsi  dan  berikut ini masing-masing adalah pemetaan dari . Tentukan rumus fungsi komposisi  dan . a.  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 open parentheses x close parentheses equals x minus 2 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 5 x 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 

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 5 x close parentheses end cell row blank equals cell open parentheses 5 x close parentheses minus 2 end cell row blank equals cell 5 x minus 2 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 open parentheses f ring operator g close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses 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 5 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 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 open parentheses g ring operator f close parentheses 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 x minus 2 close parentheses end cell row blank equals cell 5 open parentheses x minus 2 close parentheses end cell row blank equals cell 5 x minus 10 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 5 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table end style 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved