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Jika , maka

Pertanyaan

Jika f open parentheses x close parentheses equals fraction numerator 4 x minus 2 over denominator 3 x plus 4 end fraction, maka f to the power of negative 1 end exponent open parentheses 2 close parentheses equals.... 

  1. 7 

  2. negative 10 

  3. 8 

  4. 14 

  5. negative 5 

Pembahasan Soal:

Diketahui f open parentheses x close parentheses equals fraction numerator 4 x minus 2 over denominator 3 x plus 4 end fraction, maka:

space space space space space space space space f open parentheses x close parentheses equals fraction numerator 4 x minus 2 over denominator 3 x plus 4 end fraction space space space space space space space space space space space space y equals fraction numerator 4 x minus 2 over denominator 3 x plus 4 end fraction y open parentheses 3 x plus 4 close parentheses equals 4 x minus 2 space 3 x y plus 4 y equals 4 x minus 2 space 3 x y minus 4 x equals negative 2 minus 4 y x open parentheses 3 y minus 4 close parentheses equals negative 2 minus 4 y space space space space space space space space space space space space space x equals fraction numerator negative 2 minus 4 y over denominator 3 y minus 4 end fraction space space space space space space f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 2 minus 4 x over denominator 3 x minus 4 end fraction 

Sehingga:

f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 2 minus 4 x over denominator 3 x minus 4 end fraction f to the power of negative 1 end exponent open parentheses 2 close parentheses equals fraction numerator negative 2 minus 4 times 2 over denominator 3 times 2 minus 4 end fraction f to the power of negative 1 end exponent open parentheses 2 close parentheses equals fraction numerator negative 2 minus 8 over denominator 6 minus 4 end fraction f to the power of negative 1 end exponent open parentheses 2 close parentheses equals fraction numerator negative 10 over denominator 2 end fraction f to the power of negative 1 end exponent open parentheses 2 close parentheses equals negative 5 

Jadi, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika , maka tentukan .

Pembahasan Soal:

Menentukan f to the power of negative 1 end exponent left parenthesis x right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 5 over denominator x minus 9 end fraction end cell row y equals cell fraction numerator 2 x minus 5 over denominator x minus 9 end fraction end cell row cell y left parenthesis x minus 9 right parenthesis end cell equals cell 2 x minus 5 end cell row cell x y minus 9 y end cell equals cell 2 x minus 5 end cell row cell x y minus 2 x end cell equals cell 9 y minus 5 end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals cell 9 y minus 5 end cell row x equals cell fraction numerator 9 y minus 5 over denominator y minus 2 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 9 y minus 5 over denominator y minus 2 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 9 x minus 5 over denominator x minus 2 end fraction end cell end table 

f to the power of negative 1 end exponent left parenthesis x right parenthesis akan memiliki nilai jika penyebutnya tidak sama dengan nol, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell not equal to 0 row x not equal to 2 end table 

Jadi, invers dari f left parenthesis x right parenthesis adalah f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 9 x minus 5 over denominator x minus 2 end fraction comma space x not equal to 2.

1

Roboguru

Jika  adalah invers dari , maka nilai

Pembahasan Soal:

Jika begin mathsize 14px style g to the power of negative 1 end exponent end style adalah invers dari begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction comma space x not equal to 4 end style, maka nilai begin mathsize 14px style g to the power of negative 1 end exponent open parentheses 4 close parentheses equals... end style 

begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction space space space space y equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction y open parentheses 4 minus x close parentheses equals 8 minus 3 x 4 y minus x y equals 8 minus 3 x 3 x minus x y equals 8 minus 4 y x open parentheses 3 minus y close parentheses equals 8 minus 4 y x equals fraction numerator 8 minus 4 y over denominator 3 minus y end fraction g to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator 8 minus 4 y over denominator 3 minus y end fraction g to the power of negative 1 end exponent open parentheses 4 close parentheses equals fraction numerator 8 minus 4 open parentheses 4 close parentheses over denominator 3 minus 4 end fraction space space space space space space space space space space space space equals 8 end style 

 

1

Roboguru

Invers dari fungsi  adalah

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 7 over denominator 3 x plus 8 end fraction end cell row y equals cell fraction numerator 2 x minus 7 over denominator 3 x plus 8 end fraction end cell row cell 3 x y plus 8 y end cell equals cell 2 x minus 7 end cell row cell 3 x y minus 2 x end cell equals cell negative 8 y minus 7 end cell row cell x left parenthesis 3 y minus 2 right parenthesis end cell equals cell negative 8 y minus 7 end cell row x equals cell fraction numerator negative 8 y minus 7 over denominator 3 y minus 2 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 negative 8 x minus 7 over denominator 3 x minus 2 end fraction end cell end table end style

1

Roboguru

Jika , maka tentukan .

Pembahasan Soal:

misal space space fraction numerator 2 x minus 5 over denominator x minus 9 end fraction equals a space space space space space space space space space space space space 2 x minus 5 equals a open parentheses x minus 9 close parentheses space space space space space space space space space space space space 2 x minus 5 equals a x minus 9 a space space space space space space space space space 2 x minus a x equals negative 9 a plus 5 space space space space space space space space space open parentheses 2 minus a close parentheses x equals negative 9 a plus 5 space space space space space space space space space space space space space space space space space space space space x equals fraction numerator negative 9 a plus 5 over denominator 2 minus a end fraction space space space space space space space space space space space space space space space space space space space space x equals fraction numerator 9 a minus 5 over denominator a minus 2 end fraction 

Jadi, f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 9 x minus 5 over denominator x minus 2 end fraction comma space x not equal to 2.

1

Roboguru

Fungsi  didefinisikan oleh . Jika  merupakan invers dari , tentukan !

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals fraction numerator x plus 4 over denominator 2 x minus 3 end fraction comma space x not equal to negative 1 half, maka fungsi invers dari f left parenthesis x right parenthesis yaitu f to the power of negative 1 end exponent left parenthesis x right parenthesis sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end cell row y equals cell fraction numerator x plus 4 over denominator 2 x minus 3 end fraction end cell row cell y open parentheses 2 x minus 3 close parentheses end cell equals cell x plus 4 end cell row cell 2 x y minus 3 y end cell equals cell x plus 4 end cell row cell 2 x y minus x end cell equals cell 4 plus 3 y end cell row cell x open parentheses 2 y minus 1 close parentheses end cell equals cell 3 y plus 4 end cell row x equals cell fraction numerator 3 y plus 4 over denominator 2 y minus 1 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction end cell end table


Dengan demikian fungsi invers dari f left parenthesis x right parenthesis equals fraction numerator x plus 4 over denominator 2 x minus 3 end fraction comma space x not equal to negative 1 half adalah table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 4 over denominator 2 x minus 1 end fraction. end cell end table

 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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