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Tentukanlah  jika diketahui: a.  dan

Pertanyaan

Tentukanlah f open parentheses x close parentheses jika diketahui:

a. g open parentheses x close parentheses equals x plus 2 dan open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x plus 1 

Pembahasan Soal:

Diketahui g open parentheses x close parentheses equals x plus 2 dan open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x plus 1, maka:

open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x plus 1 space space space f open parentheses g open parentheses x close parentheses close parentheses equals 2 x plus 1 space space f open parentheses x plus 2 close parentheses equals 2 x plus 1 

Misalkan:

x plus 2 equals a space space space space space x equals a minus 2 

Sehingga:

f open parentheses x plus 2 close parentheses equals 2 x plus 1 space space space space space f open parentheses a close parentheses equals 2 open parentheses a minus 2 close parentheses plus 1 space space space space space f open parentheses a close parentheses equals 2 a minus 4 plus 1 space space space space space f open parentheses a close parentheses equals 2 a minus 3 space space space space space f open parentheses x close parentheses equals 2 x minus 3 

Jadi, fungsi f open parentheses x close parentheses adalah 2 x minus 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika  dan  maka

Pembahasan Soal:

Diketahui open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 10 x squared minus 8 x minus 3 dan g open parentheses x close parentheses equals 2 x plus 4 maka:

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 10 x squared minus 8 x minus 3 end cell equals cell f left parenthesis 2 x plus 4 right parenthesis end cell row cell misal space 2 x plus 4 end cell equals cell y comma space maka space x equals fraction numerator y minus 4 over denominator 2 end fraction end cell row cell 10 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses squared minus 8 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses minus 3 end cell equals cell f open parentheses 2 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses plus 4 close parentheses end cell row cell 10 open parentheses fraction numerator y squared minus 8 y plus 16 over denominator 4 end fraction close parentheses minus 4 y plus 16 minus 3 end cell equals cell f left parenthesis y right parenthesis end cell row cell fraction numerator 10 y squared over denominator 4 end fraction minus fraction numerator 80 y over denominator 4 end fraction plus 160 over 4 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 20 y plus 40 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 24 y plus 53 end cell equals cell f left parenthesis y right parenthesis end cell row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell row y equals cell 5 over 2 x squared minus 24 x plus 53 end cell row cell 2 y end cell equals cell 5 x squared minus 48 x plus 106 end cell end table

Error converting from MathML to accessible text.

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative left parenthesis negative 48 right parenthesis plus-or-minus square root of left parenthesis negative 48 right parenthesis squared minus 4 left parenthesis 5 right parenthesis left parenthesis 106 minus 2 y right parenthesis end root over denominator 2 left parenthesis 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 2.304 minus 2.120 plus 40 y end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 40 y plus 184 end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 10 end fraction end cell row blank equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table 

Jadi jawabannya tidak ada pada opsi, jawaban yang benar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent 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 cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table 

0

Roboguru

Diketahui fungsi  dan . Hasil dari  adalah ...

Pembahasan Soal:

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 4 x squared minus 6 x plus 11 end cell row cell f left parenthesis 2 x squared minus 3 x plus 1 right parenthesis end cell equals cell 4 x squared minus 6 x plus 11 end cell row blank blank blank row cell 2 x squared minus 3 x plus 1 end cell equals a row cell 2 x squared minus 3 x end cell equals cell a minus 1 end cell row blank blank blank row cell f left parenthesis 2 x squared minus 3 x plus 1 right parenthesis end cell equals cell 4 x squared minus 6 x plus 11 end cell row cell f left parenthesis 2 x squared minus 3 x plus 1 right parenthesis end cell equals cell 2 left parenthesis 2 x squared minus 3 x right parenthesis plus 11 end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a minus 1 right parenthesis plus 11 end cell row blank equals cell 2 a minus 2 plus 11 end cell row blank equals cell 2 a plus 9 end cell row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 9 end cell end table end style

0

Roboguru

Jika  dan , maka

Pembahasan Soal:

Diketahui g left parenthesis x right parenthesis equals 2 x plus 1 dan open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals 4 x squared plus 4 x plus 5, maka:

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 4 x squared plus 4 x plus 5 end cell row cell f left parenthesis 2 x plus 1 right parenthesis end cell equals cell 4 x squared plus 4 x plus 5 end cell row cell misal space a end cell equals cell space 2 x plus 1 comma space maka space x equals space fraction numerator a minus 1 over denominator 2 end fraction end cell row cell f left parenthesis a right parenthesis end cell equals cell 4 open parentheses fraction numerator a minus 1 over denominator 2 end fraction close parentheses squared plus 4 open parentheses fraction numerator a minus 1 over denominator 2 end fraction close parentheses plus 5 end cell row cell f left parenthesis a right parenthesis end cell equals cell 4 open parentheses fraction numerator a squared minus 2 a plus 1 over denominator 4 end fraction close parentheses plus 2 left parenthesis a minus 1 right parenthesis plus 5 end cell row cell f left parenthesis a right parenthesis end cell equals cell a squared minus 2 a plus 1 plus 2 a minus 2 plus 5 end cell row cell f left parenthesis a right parenthesis end cell equals cell a squared plus 4 end cell row cell f left parenthesis x right parenthesis end cell equals cell x squared plus 4 end cell row blank blank blank end table

Jadi, jawaban yang tepat adalah A 

0

Roboguru

Tentukan  jika: c.

Pembahasan Soal:

Diketahui:

Fungsi begin mathsize 14px style open parentheses f open parentheses x close parentheses close parentheses squared plus 5 equals 9 x minus 4 end style

Diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f open parentheses x close parentheses close parentheses squared plus 5 end cell equals cell 9 x minus 4 end cell row cell open parentheses f open parentheses x close parentheses close parentheses squared end cell equals cell 9 x minus 4 minus 5 end cell row cell open parentheses f open parentheses x close parentheses close parentheses squared end cell equals cell 9 x minus 9 end cell row cell open parentheses f open parentheses x close parentheses close parentheses squared end cell equals cell 9 open parentheses x minus 1 close parentheses end cell row cell square root of open parentheses f open parentheses x close parentheses close parentheses squared end root end cell equals cell plus-or-minus square root of 9 open parentheses x minus 1 close parentheses end root end cell row cell f open parentheses x close parentheses end cell equals cell plus-or-minus square root of 9 open parentheses x minus 1 close parentheses end root end cell row cell f open parentheses x close parentheses end cell equals cell plus-or-minus 3 square root of x minus 1 end root end cell end table end style

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 square root of x minus 1 end root end cell row cell f open parentheses x close parentheses end cell equals cell negative 3 square root of x minus 1 end root end cell end table end style

0

Roboguru

Diketahui dan . Tentukan rumus fungsi !

Pembahasan Soal:

Komposisi fungsi merupakan penggabungan operasi dua jenis fungsi sehingga menghasilkan sebuah fungsi baru.

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 8 x squared plus 4 x plus 6 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 8 x squared plus 4 x plus 6 end cell row cell f open parentheses 2 x plus 2 close parentheses end cell equals cell 8 x squared plus 4 x plus 6 end cell end table

Lalu kita misalkan 2 x plus 2 equals y, maka x equals fraction numerator y minus 2 over denominator 2 end fraction. Kemudian kita substitusi ke persamaan sebelumnya.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses y close parentheses end cell equals cell 8 open parentheses fraction numerator y minus 2 over denominator 2 end fraction close parentheses squared plus 4 open parentheses fraction numerator y minus 2 over denominator 2 end fraction close parentheses plus 6 end cell row blank equals cell 8 open parentheses fraction numerator y squared minus 4 y plus 4 over denominator 4 end fraction close parentheses plus 2 y minus 4 plus 6 end cell row blank equals cell 2 y squared minus 8 y plus 8 plus 2 y minus 4 plus 6 end cell row blank equals cell 2 y squared minus 6 y plus 10 end cell end table

Setelah itu ubah y menjadi x, maka f open parentheses x close parentheses equals 2 x squared minus 6 x plus 10.

Jadi, rumus fungsi f open parentheses x close parentheses adalah 2 x squared minus 6 x plus 10.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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