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Pertanyaan

Jika f left parenthesis x right parenthesis equals fraction numerator negative 2 x plus 4 over denominator x minus 6 end fraction semicolon x not equal to 6 maka f to the power of negative 1 end exponent open parentheses x close parentheses equals... space. 

  1. fraction numerator negative 6 x plus 4 over denominator x minus 2 end fraction semicolon x not equal to 2

  2. fraction numerator negative x plus 2 over denominator x minus 6 end fraction semicolon x not equal to 6 

  3. fraction numerator x minus 6 over denominator x plus 4 end fraction semicolon x not equal to negative 4 

  4. fraction numerator negative 6 x plus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2 

  5. fraction numerator 6 x plus 4 over denominator x plus 2 end fraction semicolon x not equal to negative 2  

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals fraction numerator negative 2 x plus 4 over denominator x minus 6 end fraction semicolon x not equal to 6 maka f to the power of negative 1 end exponent open parentheses x close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 4 over denominator x minus 6 end fraction end cell row y equals cell fraction numerator negative 2 x plus 4 over denominator x minus 6 end fraction end cell row cell y open parentheses x minus 6 close parentheses end cell equals cell negative 2 x plus 4 end cell row cell x y minus 6 y end cell equals cell negative 2 x plus 4 end cell row cell x y plus 2 x end cell equals cell 4 plus 6 y end cell row cell x open parentheses y plus 2 close parentheses end cell equals cell 4 plus 6 y end cell row x equals cell fraction numerator 4 plus 6 y over denominator y plus 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator 4 plus 6 y over denominator y plus 2 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 4 plus 6 x over denominator x plus 2 end fraction end cell row blank equals cell fraction numerator 6 x plus 4 over denominator x plus 2 end fraction end cell end table

Kemudian, f to the power of negative 1 end exponent open parentheses x close parentheses di atas terdefinisi saat x plus 2 not equal to 0x plus 2 not equal to 0maka x not equal to negative 2. Oleh karena itu, f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 x plus 4 over denominator x plus 2 end fraction dengan x not equal to negative 2


Jadi, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 02 Mei 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

Tentukan fungsi invers dari fungsi sebagai berikut: 2)

Pembahasan Soal:

Bentuk umum fungsi invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction end style adalah begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative d x plus b over denominator c x minus a end fraction end style.

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 x minus 4 over denominator 3 x plus 8 end fraction end style, dengan nilai begin mathsize 14px style a equals 2 comma space b equals negative 4 comma end style begin mathsize 14px style c equals 3 comma space dan space d equals 8 end style.

Dengan demikian, fungsi inversnya adalah

begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 8 x minus 4 over denominator 3 x minus 2 end fraction end style.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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