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dan , rumus fungsi  adalah ....

Pertanyaan

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x squared plus 8 x minus 11 end style dan begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 5 end style, rumus fungsi begin mathsize 14px style g open parentheses x close parentheses end style adalah ....

Pembahasan Soal:

Dengan menerapkan konsep komposisi dua fungsi, diperoleh perhitungan sebagai berikut.

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 4 x squared plus 8 x minus 11 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x squared plus 8 x minus 11 end cell row cell 2 g open parentheses x close parentheses minus 5 end cell equals cell 4 x squared plus 8 x minus 11 end cell row cell 2 g open parentheses x close parentheses end cell equals cell 4 x squared plus 8 x minus 11 plus 5 end cell row blank equals cell 4 x squared plus 8 x minus 6 end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 4 x squared plus 8 x minus 6 over denominator 2 end fraction end cell row blank equals cell 2 x squared plus 4 x minus 3 end cell end table end style 

Jadi, rumus fungsi begin mathsize 14px style g open parentheses x close parentheses end style adalah begin mathsize 14px style g open parentheses x close parentheses equals 2 x squared plus 4 x minus 3 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 29 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diberikan dan , maka fungsi

Pembahasan Soal:

DIketahui: left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 4 x plus 6 ; f left parenthesis x right parenthesis equals 2 x minus 4

Ditanya: g left parenthesis x right parenthesis?

Jawab:

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 4 x plus 6 end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 4 x plus 6 end cell row cell 2 left parenthesis g left parenthesis x right parenthesis right parenthesis minus 4 end cell equals cell 4 x plus 6 end cell row cell 2 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 4 x plus 6 plus 4 end cell row cell 2 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 4 x plus 10 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x plus 10 over denominator 2 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x plus 5 end cell end table

Jadi, g left parenthesis x right parenthesis equals 2 x plus 5.

0

Roboguru

Jika diketahui  dan , nilai fungsi  adalah

Pembahasan Soal:

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 18 x squared minus 24 x plus 9 end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 18 x squared minus 24 x plus 9 end cell row cell 2 open parentheses g left parenthesis x right parenthesis close parentheses squared plus 8 open parentheses g left parenthesis x right parenthesis close parentheses plus 1 end cell equals cell 18 x squared minus 24 x plus 9 end cell end table

Misalnya: g left parenthesis x right parenthesis equals straight a x plus straight b

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open parentheses straight g left parenthesis straight x right parenthesis close parentheses squared plus 8 open parentheses straight g left parenthesis straight x right parenthesis close parentheses plus 1 end cell equals cell 18 straight x squared minus 24 straight x plus 9 end cell row cell 2 open parentheses ax plus straight b close parentheses squared plus 8 open parentheses ax plus straight b close parentheses plus 1 end cell equals cell 18 straight x squared minus 24 straight x plus 9 end cell row cell 2 open parentheses straight a squared straight x squared plus 2 abx plus straight b squared close parentheses plus 8 ax plus 8 straight b plus 1 end cell equals cell 18 straight x squared minus 24 straight x plus 9 end cell row cell 2 straight a squared straight x squared plus left parenthesis 4 ab plus 8 straight a right parenthesis straight x plus 2 straight b squared plus 8 straight b plus 1 end cell equals cell 18 straight x squared minus 24 straight x plus 9 end cell end table

Dari kesamaan suku banyak diatas diperoleh: 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight a squared end cell equals 18 row cell straight a squared end cell equals 9 row straight a equals cell plus-or-minus square root of 9 end cell row straight a equals cell plus-or-minus 3 end cell end table 

untuk straight a equals 3 maka: 

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 ab plus 8 straight a end cell equals cell negative 24 end cell row cell 4 left parenthesis 3 right parenthesis straight b plus 8 left parenthesis 3 right parenthesis end cell equals cell negative 24 end cell row cell 12 straight b plus 24 end cell equals cell negative 24 end cell row cell 12 straight b end cell equals cell negative 48 end cell row straight b equals cell negative 4 end cell end table

g left parenthesis x right parenthesis equals 3 x minus 4 g left parenthesis 5 right parenthesis equals 3 left parenthesis 5 right parenthesis minus 4 g left parenthesis 5 right parenthesis equals 15 minus 4 g left parenthesis 5 right parenthesis equals 11

untuk straight a equals negative 3, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 ab plus 8 straight a end cell equals cell negative 24 end cell row cell 4 left parenthesis negative 3 right parenthesis straight b plus 8 left parenthesis negative 3 right parenthesis end cell equals cell negative 24 end cell row cell negative 12 straight b minus 24 end cell equals cell negative 24 end cell row cell negative 12 straight b end cell equals 0 row straight b equals 0 end table

g left parenthesis x right parenthesis equals negative 3 x minus 0 g left parenthesis 5 right parenthesis equals negative 3 left parenthesis 5 right parenthesis g left parenthesis 5 right parenthesis equals negative 15 g left parenthesis 5 right parenthesis equals negative 15

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Diketahui  dan . Tentukan .

Pembahasan Soal:

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 2 x squared plus 4 x plus 11 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 2 x squared plus 4 x plus 11 end cell row cell 2 g open parentheses x close parentheses plus 1 end cell equals cell 2 x squared plus 4 x plus 11 end cell row cell 2 g open parentheses x close parentheses end cell equals cell 2 x squared plus 4 x plus 10 end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 2 x squared plus 4 x plus 10 over denominator 2 end fraction end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 2 x plus 5 end cell end table 

Dengan demikian, fungsi g open parentheses x close parentheses adalah x squared plus 2 x plus 5.

0

Roboguru

Diketahui fungsi  yang dirumuskan oleh  dan . Rumus fungsi  adalah ....

Pembahasan Soal:

Dengan menggunakan fungsi komposisi, maka didapat:

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 4 x squared minus 24 x plus 32 end cell row cell g open parentheses 2 x minus 4 close parentheses end cell equals cell 4 x squared minus 24 x plus 32 end cell row blank blank blank row cell misal comma space 2 x minus 4 end cell equals a row cell 2 x end cell equals cell a plus 4 end cell row x equals cell fraction numerator a plus 4 over denominator 2 end fraction end cell row blank blank blank row cell g open parentheses a close parentheses end cell equals cell 4 open parentheses fraction numerator a plus 4 over denominator 2 end fraction close parentheses squared minus 24 open parentheses fraction numerator a plus 4 over denominator 2 end fraction close parentheses plus 32 end cell row blank equals cell 4 open parentheses fraction numerator a squared plus 8 a plus 16 over denominator 4 end fraction close parentheses minus 12 open parentheses a plus 4 close parentheses plus 32 end cell row blank equals cell a squared plus 8 a plus 16 minus 12 a minus 48 plus 32 end cell row blank equals cell a squared minus 4 a end cell row cell g open parentheses x close parentheses end cell equals cell x squared minus 4 x end cell end table end style

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Jika  dan , maka ....

Pembahasan Soal:

Kita mempunyai

begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator 3 x plus 1 end fraction left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator x over denominator 3 x minus 2 end fraction end style 

Kemudian, perhatikan perhitungan berikut!

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 fraction numerator x over denominator 3 x minus 2 end fraction end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell fraction numerator x over denominator 3 x minus 2 end fraction end cell row cell fraction numerator 1 over denominator 3 times g open parentheses x close parentheses plus 1 end fraction end cell equals cell fraction numerator x over denominator 3 x minus 2 end fraction end cell row cell 3 times g open parentheses x close parentheses plus 1 end cell equals cell fraction numerator 3 x minus 2 over denominator x end fraction end cell row cell 3 times g open parentheses x close parentheses end cell equals cell fraction numerator 3 x minus 2 over denominator x end fraction minus 1 end cell row cell 3 times g open parentheses x close parentheses end cell equals cell fraction numerator 2 x minus 2 over denominator x end fraction end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 2 x minus 2 over denominator 3 x end fraction end cell row cell g open parentheses x close parentheses end cell equals cell 2 over 3 open parentheses 1 minus 1 over x close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah B.

0

Roboguru

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