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Pertanyaan

Invers dari f left parenthesis x right parenthesis equals fraction numerator 9 x minus 2 over denominator 3 x plus 6 end fraction adalah ...

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals fraction numerator 9 x minus 2 over denominator 3 x plus 6 end fraction, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 9 x minus 2 over denominator 3 x plus 6 end fraction end cell row y equals cell fraction numerator 9 x minus 2 over denominator 3 x plus 6 end fraction end cell row cell y left parenthesis 3 x plus 6 right parenthesis end cell equals cell 9 x minus 2 end cell row cell 3 x y plus 6 y end cell equals cell 9 x minus 2 end cell row cell 3 x y minus 9 x end cell equals cell negative 6 y minus 2 end cell row cell x left parenthesis 3 y minus 9 right parenthesis end cell equals cell negative 6 y minus 2 end cell row x equals cell fraction numerator negative 6 y minus 2 over denominator 3 y minus 9 end fraction end cell row x equals cell fraction numerator 6 y plus 2 over denominator negative 3 y plus 9 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 6 x plus 2 over denominator negative 3 x plus 9 end fraction end cell end table 

Jadi, invers dari f left parenthesis x right parenthesis equals fraction numerator 9 x minus 2 over denominator 3 x plus 6 end fraction 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 6 x plus 2 over denominator negative 3 x plus 9 end fraction end cell end table 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Fungsi   ditentukan oleh  , maka  ...

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator 2 x minus 1 end fraction semicolon space x not equal to 1 half, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 2 over denominator 2 x minus 1 end fraction end cell row y equals cell fraction numerator 3 x plus 2 over denominator 2 x minus 1 end fraction end cell row cell y left parenthesis 2 x minus 1 right parenthesis end cell equals cell 3 x plus 2 end cell row cell 2 x y minus y end cell equals cell 3 x plus 2 end cell row cell 2 x y minus 3 x end cell equals cell y plus 2 end cell row cell x left parenthesis 2 y minus 3 right parenthesis end cell equals cell y plus 2 end cell row x equals cell fraction numerator y plus 2 over denominator 2 y minus 3 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 x plus 2 over denominator 2 x minus 3 end fraction semicolon space x not equal to 3 over 2 end cell end table 

Jadi, jawaban yang tepat adalah D

0

Roboguru

Tentukan invers dari fungsi-fungsi berikut ini! a.

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals 2 x plus 7, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 7 end cell row y equals cell 2 x plus 7 end cell row cell y minus 7 end cell equals cell 2 x end cell row cell fraction numerator y minus 7 over denominator 2 end fraction end cell equals x row x equals cell fraction numerator y minus 7 over denominator 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 x minus 7 over denominator 2 end fraction end cell end table

Jadi, invers fungsi f left parenthesis x right parenthesis equals 2 x plus 7 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 x minus 7 over denominator 2 end fraction end cell end table 

0

Roboguru

Diketahui fungsi . Invers fungsi dari  adalah ...

Pembahasan Soal:

Diketahui:

f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2

Mencari invers fungsi f 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 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2 end cell row y equals cell fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction end cell row x equals cell fraction numerator 4 y minus 5 over denominator 2 y plus 9 end fraction end cell row cell x left parenthesis 2 y plus 9 right parenthesis end cell equals cell 4 y minus 5 end cell row cell 2 x y plus 9 x end cell equals cell 4 y minus 5 end cell row cell 2 x y minus 4 y end cell equals cell negative 9 x minus 5 end cell row cell 2 y left parenthesis x minus 2 right parenthesis end cell equals cell negative 9 x minus 5 end cell row cell 2 y end cell equals cell fraction numerator negative 9 x minus 5 over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row y equals cell fraction numerator negative 9 x minus 5 over denominator 2 left parenthesis x minus 2 right parenthesis end fraction end cell row y equals cell fraction numerator negative 9 x minus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell negative fraction numerator 9 x plus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end cell end table 

Jadi, invers fungsi f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2 adalah f to the power of negative 1 end exponent equals negative fraction numerator 9 x plus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2.

Dengan demikian, jawaban yang tepat adalah C.

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

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

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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