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Diketahui , maka  adalah...

Pertanyaan

Diketahui f open parentheses x close parentheses equals x squared comma space g open parentheses x close parentheses equals negative x minus 2 comma space dan space h open parentheses x close parentheses equals 2 x squared plus 3, maka open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses adalah...

  1. negative 4 x to the power of 4 minus 20 x squared plus 25

  2. 4 x to the power of 4 plus 4 x squared plus 1

  3. 4 x to the power of 4 plus 8 x squared plus 1

  4. 4 x to the power of 4 plus 20 x squared plus 25

  5. negative 4 x to the power of 4 plus 20 x squared plus 25

Pembahasan Soal:

Dengan menggunakan konsep fungsi komposisi diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses 2 x squared plus 3 close parentheses close parentheses end cell row blank equals cell f open parentheses negative open parentheses 2 x squared plus 3 close parentheses minus 2 close parentheses end cell row blank equals cell f open parentheses negative 2 x squared minus 3 minus 2 close parentheses end cell row blank equals cell f open parentheses negative 2 x squared minus 5 close parentheses end cell row blank equals cell open parentheses negative 2 x squared minus 5 close parentheses squared end cell row blank equals cell 4 x to the power of 4 plus 20 x squared plus 25 end cell end table

Dengan demikian Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Nur

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

Jika , , dan , tentukan hasil dari !

Pembahasan Soal:

Dengan menggunakan konsep komposisi tiga fungsi maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses fraction numerator 3 x plus 5 over denominator 4 end fraction close parentheses close parentheses end cell row blank equals cell f open parentheses 2 open parentheses fraction numerator 3 x plus 5 over denominator 4 end fraction close parentheses minus 3 close parentheses end cell row blank equals cell f open parentheses fraction numerator 3 x plus 5 over denominator 2 end fraction minus 3 close parentheses end cell row blank equals cell f open parentheses fraction numerator 3 x plus 5 minus 6 over denominator 2 end fraction close parentheses end cell row blank equals cell f open parentheses fraction numerator 3 x minus 1 over denominator 2 end fraction close parentheses end cell row blank equals cell 4 open parentheses fraction numerator 3 x minus 1 over denominator 2 end fraction close parentheses plus 1 end cell row blank equals cell 2 open parentheses 3 x minus 1 close parentheses plus 1 end cell row blank equals cell 6 x minus 2 plus 1 end cell row blank equals cell 6 x minus 1 end cell end table end style 

Dengan demikian, hasil dari begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end style adalah begin mathsize 14px style 6 x minus 1 end style.

0

Roboguru

Jika , , dan , komposisi fungsi

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus 2 x plus 3 end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals x plus 2 end style, dan begin mathsize 14px style h left parenthesis x right parenthesis equals 2 x minus 1 end style.

Pertama, hitung terlebih dahulu fungsi komposisi begin mathsize 14px style open parentheses g ring operator h 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 h close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis h left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis 2 x minus 1 right parenthesis end cell row blank equals cell left parenthesis 2 x minus 1 right parenthesis plus 2 end cell row blank equals cell 2 x plus 1 end cell end table end style 

Selanjutnya, komposisi dari tiga fungsi dapat dicari dengan mensubstitusikan fungsi begin mathsize 14px style x end style pada begin mathsize 14px style f left parenthesis x right parenthesis end style dengan fungsi komposisi begin mathsize 14px style open parentheses g ring operator h close parentheses left parenthesis x right parenthesis end style seperti berikut,

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

Dengan demikian, komposisi dari tiga fungsi begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses left parenthesis x right parenthesis end style adalah Error converting from MathML to accessible text..

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Diketahui fungsi , , dan . Tentukan : b.  dan

Pembahasan Soal:

Terlebih dahulu dihitung fungsi komposisi begin mathsize 14px style open parentheses f ring operator h close parentheses left parenthesis x right parenthesis end style, yaitu 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator h close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis h left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f open parentheses x squared minus 1 close parentheses end cell row blank equals cell open parentheses x squared minus 1 close parentheses plus 2 end cell row blank equals cell x squared plus 1 end cell end table end style 

Komposisi dari ketiga fungsi di atas dapat dihitung dengan mensubstitusikan fungsi begin mathsize 14px style left parenthesis f ring operator h right parenthesis end style size 14px left parenthesis size 14px x size 14px right parenthesis ke dalam fungsi begin mathsize 14px style g left parenthesis x right parenthesis end style seperti berikut,

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

Dengan demikian, fungsi komposisi begin mathsize 14px style open parentheses g ring operator f ring operator h close parentheses left parenthesis x right parenthesis end style adalah begin mathsize 14px style 3 x squared plus 2 end style.

Selanjutnya nilai undefined disubstitusikan ke dalam fungsi komposisi sehingga didapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f ring operator h close parentheses left parenthesis 3 right parenthesis end cell equals cell 3 times 3 squared plus 2 end cell row blank equals cell 27 plus 2 end cell row blank equals 29 end table end style 

Jadi, nilai dari undefined adalah begin mathsize 14px style 29 end style.

0

Roboguru

1. Diket :  Tentukan a.

Pembahasan Soal:

Diketahui :

straight f open parentheses straight x close parentheses equals straight x space plus 3 straight g open parentheses straight x close parentheses equals 2 straight x space minus 1 straight h open parentheses straight x close parentheses equals straight x squared

Ditanya :

open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses

Penyelesaian 

Akan dicari hasil dari komposisi open parentheses straight g ring operator straight h close parentheses open parentheses straight x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight g ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight h open parentheses straight x close parentheses close parentheses end cell row blank equals cell 2 open parentheses straight x squared close parentheses minus 1 end cell row blank equals cell 2 straight x squared minus 1 end cell end table

Selanjutnya akan dicari hasil komposisi dari open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell straight f open parentheses straight g ring operator straight h close parentheses open parentheses straight x close parentheses end cell row blank equals cell straight f open parentheses 2 straight x squared minus 1 close parentheses open parentheses straight x close parentheses end cell row blank equals cell left parenthesis 2 x squared minus 1 right parenthesis plus 3 end cell row blank equals cell 2 straight x squared minus 1 plus 3 end cell row blank equals cell 2 straight x squared plus 2 end cell row blank equals cell 2 left parenthesis straight x squared plus 1 right parenthesis end cell end table

Jadi, hasil komposisi fungsi open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses equals 2 left parenthesis straight x squared plus 1 right parenthesis

0

Roboguru

1. Diket : Tentukan  b)

Pembahasan Soal:

Diketahui :

straight f open parentheses straight x close parentheses equals straight x plus 3 straight g open parentheses straight x close parentheses equals 2 straight x minus 1 straight h open parentheses straight x close parentheses equals straight x squared

Ditanya :

open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses 3 close parentheses

Penyelesaian 

open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses 3 close parentheses

Akan dicari fungsi komposisi dari open parentheses g ring operator f close parentheses open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight f open parentheses straight x close parentheses close parentheses end cell row blank equals cell 2 open parentheses straight x plus 3 close parentheses minus 1 end cell row blank equals cell 2 straight x plus 6 minus 1 end cell row blank equals cell 2 straight x plus 5 end cell end table

selanjutnya akan dicari komposisi fungsi dari open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses straight x close parentheses end cell equals cell straight h open parentheses straight g ring operator straight f open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight h open parentheses 2 straight x plus 5 close parentheses end cell row blank equals cell open parentheses 2 straight x plus 5 close parentheses squared end cell row blank equals cell 4 straight x squared plus 20 straight x plus 25 end cell end table

Akan dicari nilai dari open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses 3 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses 3 close parentheses end cell equals cell 4 open parentheses 3 close parentheses squared plus 20 open parentheses 3 close parentheses plus 25 end cell row blank equals cell 4 open parentheses 9 close parentheses plus 60 plus 25 end cell row blank equals cell 36 plus 60 plus 25 end cell row blank equals 121 end table

Jadi, nilai dari open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses 3 close parentheses equals 121.

0

Roboguru

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