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Diketahui f(x)=x2+4x+4 dan g(x)=x2−4x+4. Rumus f(g(x))​+g(f(x))​=....

Pertanyaan

Diketahui  dan . Rumus  

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Pembahasan Video:

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

 

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Ayudhita

Terakhir diupdate 05 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika f(x) = x−2 dan g(x)=x+2, fungsi {(f∘g)(x)}⋅{(g∘f(x))}=....

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 fungsi f(x)=3x−1 dan g(x)=2x2+4x−10. Nilai dari komposisi fungsi (g∘f)(−2) adalah ....

Pembahasan Soal:

Jika diberikan fungsi f open parentheses x close parentheses space dan space g open parentheses x close parentheses maka dapat ditentukan fungsi komposisi dan nilai dari fungsi komposisi tersebut sebagai 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 cell open parentheses g ring operator f close parentheses open parentheses n close parentheses end cell equals cell g open parentheses f open parentheses n close parentheses close parentheses end cell end table 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 x minus 1 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x squared plus 4 x minus 10 end cell end table 

Sehingga dapat ditentukan:

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 2 times open parentheses f open parentheses x close parentheses close parentheses squared plus 4 times f open parentheses x close parentheses minus 10 end cell row blank equals cell 2 times open parentheses 3 x minus 1 close parentheses squared plus 4 times open parentheses 3 x minus 1 close parentheses minus 10 end cell row blank equals cell 2 times open parentheses 9 x squared minus 6 x plus 1 close parentheses plus 12 x minus 4 minus 10 end cell row blank equals cell 18 x squared minus 12 x plus 2 plus 12 x minus 4 minus 10 end cell row blank equals cell 18 x squared minus 12 end cell row cell open parentheses g ring operator f close parentheses open parentheses negative 2 close parentheses end cell equals cell g open parentheses f open parentheses negative 2 close parentheses close parentheses end cell row blank equals cell 18 times open parentheses negative 2 close parentheses squared minus 12 end cell row blank equals cell 18 times 4 minus 12 end cell row blank equals cell 72 minus 12 end cell row blank equals 60 end table 

Dengan demikian, diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 2 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 60 end table.

0

Roboguru

Diketahu fungsi f(x)=3x−1 dan g(x)=2x2+4x−10. Nilai dari komposisi fungsi (g∘f)(−2) ...

Pembahasan Soal:

Tentukan terlebih dahulu komposisi fungsi open parentheses g ring operator f close parentheses open parentheses x close parentheses.

Fungsi open parentheses g ring operator f close parentheses open parentheses x close parentheses adalah komposisi fungsi dari penggabungan dua jenis fungsi g open parentheses x close parentheses terhadap f open parentheses x close parentheses sehingga menghasilkan fungsi yang baru.

Sehingga diperoleh:

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 minus 1 close parentheses end cell row blank equals cell 2 open parentheses 3 x minus 1 close parentheses squared plus 4 open parentheses 3 x minus 1 close parentheses minus 10 end cell row blank equals cell 2 open parentheses 9 x squared minus 6 x plus 1 close parentheses plus 12 x minus 4 minus 10 end cell row blank equals cell 18 x squared minus 12 x plus 2 plus 12 x minus 14 end cell row blank equals cell 18 x squared minus 12 end cell end table

Kemudian substitusi variabel x pada fungsi open parentheses g ring operator f close parentheses open parentheses x close parentheses dengan 2 seperti 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 18 x squared minus 12 end cell row cell open parentheses g ring operator f close parentheses open parentheses 2 close parentheses end cell equals cell 18 open parentheses 2 close parentheses squared minus 12 end cell row blank equals cell 18 open parentheses 4 close parentheses minus 12 end cell row blank equals cell 72 minus 12 end cell row blank equals 60 end table

Maka, nilai dari komposisi fungsi open parentheses g ring operator f close parentheses open parentheses negative 2 close parentheses adalah 60.

0

Roboguru

Diketahui  f(x)=2x2−3x+4 dan g(x)=4x−5. Nilai dari fungsi (g∘f)(2) adalah ...

Pembahasan Soal:

Pertama akan dicari fungsi komposisi begin mathsize 14px style open parentheses g ring operator f 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 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 cell space space space space space space space space space space space space space end cell equals cell g open parentheses 2 x squared minus 3 x plus 4 close parentheses end cell row cell space space space space space space space space space space space space space end cell equals cell 4 open parentheses 2 x squared minus 3 x plus 4 close parentheses minus 5 end cell row cell space space space space space space space space space space space space space end cell equals cell 8 x squared minus 12 x plus 16 minus 5 end cell row cell space space space space space space space space space space space space space end cell equals cell 8 x squared minus 12 x plus 11 end cell end table end style   

Selanjutnya akan ditentukan nilai fungsi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses 2 close parentheses end style 

begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses 2 close parentheses equals 8 open parentheses 2 close parentheses squared minus 12 open parentheses 2 close parentheses plus 11 space space space space space space space space space space space space space equals 32 minus 24 plus 11 space space space space space space space space space space space space space equals 19 end style 

Jadi,jawaban yang tepat adalah D

0

Roboguru

Diketahui  f(x+2)=2x+6 dan g(x)=2x2−7x−12. Nilai dari fungsi (g∘f)(−3) adalah ...

Pembahasan Soal:

Pertama akan dicari fungsi begin mathsize 14px style f open parentheses x close parentheses end style  dengan cara berikut.

begin mathsize 14px style f open parentheses x plus 2 close parentheses equals 2 x plus 6 end style 

misal begin mathsize 14px style a equals x plus 2 left right double arrow x equals a minus 2 end style 

begin mathsize 14px style f open parentheses a close parentheses equals 2 open parentheses a minus 2 close parentheses plus 6 space space space space space space equals 2 a minus 4 plus 6 space space space space space space equals 2 a plus 2 f open parentheses x close parentheses equals 2 x plus 2 end style 

Selanjutnya akan ditentukan  begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses end style  

begin mathsize 14px style 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 equals g open parentheses 2 x divided by 2 close parentheses space space space space space space space space space space space space space equals 2 open parentheses 2 x plus 2 close parentheses squared minus 7 open parentheses 2 x plus 2 close parentheses minus 12 space space space space space space space space space space space space space equals 2 open parentheses 4 x squared plus 8 x plus 4 close parentheses minus 14 x minus 14 minus 12 space space space space space space space space space space space space space equals 8 x squared plus 16 x plus 8 minus 14 x minus 26 space space space space space space space space space space space space space equals 8 x squared plus 2 x minus 18 end style 

Nilai  dari  fungsi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses negative 3 close parentheses end style

begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses negative 3 close parentheses equals 8 open parentheses negative 3 close parentheses squared plus 2 open parentheses negative 3 close parentheses minus 18 space space space space space space space space space space space space space space space space equals 8 open parentheses 9 close parentheses minus 6 minus 18 space space space space space space space space space space space space space space space space equals 72 minus 6 minus 18 space space space space space space space space space space space space space space space space equals 48 end style 

Jadi,jawaban yang tepat adalah E

0

Roboguru

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