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Pertanyaan

Diketahui f open parentheses x close parentheses equals fraction numerator negative 4 x plus 3 over denominator x minus 1 end fraction comma space x not equal to 1 dan g open parentheses x close parentheses equals x plus 2. Maka open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses!

  1. fraction numerator x plus 2 over denominator x plus 1 end fraction comma space x not equal to 1

  2. fraction numerator x plus 1 over denominator x plus 2 end fraction comma space x not equal to negative 2

  3. fraction numerator x minus 3 over denominator x minus 2 end fraction comma space x not equal to 2

  4. fraction numerator x plus 3 over denominator x plus 2 end fraction comma space x not equal to negative 2

  5. fraction numerator negative x plus 3 over denominator x minus 1 end fraction comma space x not equal to negative 1

Pembahasan Soal:

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 4 x plus 3 over denominator x minus 1 end fraction comma space g open parentheses x close parentheses equals x plus 2 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell x plus 2 end cell row blank equals cell fraction numerator negative 4 x plus 3 over denominator x minus 1 end fraction plus 2 end cell row blank equals cell fraction numerator negative 4 x plus 3 plus 2 x minus 2 over denominator x minus 1 end fraction end cell row blank equals cell fraction numerator negative 2 x plus 1 over denominator x minus 1 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 1 over denominator x plus 2 end fraction comma space x not equal to negative 2 end cell end table

Jadi, Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan . Tentukan :

Pembahasan Soal:

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 5 x minus 1 comma space g left parenthesis x right parenthesis equals x plus 3 end style, sehingga didapat :

begin mathsize 14px style 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 blank equals cell 5 left parenthesis g left parenthesis x right parenthesis right parenthesis minus 1 end cell row blank equals cell 5 left parenthesis x plus 3 right parenthesis minus 1 end cell row blank equals cell 5 x plus 15 minus 1 end cell row blank equals cell 5 x plus 14 end cell row blank blank blank end table end style 

Misalkan begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals y end style, maka didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 5 x plus 14 end cell row cell 5 x end cell equals cell y minus 14 end cell row x equals cell fraction numerator y minus 14 over denominator 5 end fraction end cell end table end style 

Dengan mengganti dengan x, maka didapat:

begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 14 over denominator 5 end fraction end style 

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Roboguru

Diketahui fungsi  dan . Jika  dengan  adalah invers fungsi  dan  adalah invers fungsi , fungsi ...

Pembahasan Soal:

Diketahui : f left parenthesis x right parenthesis equals 2 x plus 4g left parenthesis x right parenthesis equals fraction numerator 2 x plus 5 over denominator x minus 4 end fraction comma space x not equal to 4h left parenthesis x right parenthesis equals left parenthesis g ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis

Cari f to the power of negative 1 end exponent left parenthesis x right parenthesis terlebih dahulu. Misal y equals f left parenthesis x right parenthesis sehingga x equals f to the power of negative 1 end exponent left parenthesis y right parenthesis 

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 4 end cell row y equals cell 2 x plus 4 end cell row cell y minus 4 end cell equals cell 2 x end cell row cell fraction numerator y minus 4 over denominator 2 end fraction end cell equals x row x equals cell fraction numerator y minus 4 over denominator 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 y minus 4 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 4 over denominator 2 end fraction end cell end table  

Cari nilai h left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell left parenthesis g ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis fraction numerator x minus 4 over denominator 2 end fraction right parenthesis end cell row blank equals cell fraction numerator 2 left parenthesis fraction numerator x minus 4 over denominator 2 end fraction right parenthesis plus 5 over denominator left parenthesis begin display style fraction numerator x minus 4 over denominator 2 end fraction end style right parenthesis minus 4 end fraction end cell row blank equals cell fraction numerator x minus 4 plus 5 over denominator begin display style fraction numerator left parenthesis x minus 4 right parenthesis minus 8 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 left parenthesis x plus 1 right parenthesis over denominator x minus 12 end fraction end cell row blank equals cell fraction numerator 2 x plus 2 over denominator x minus 12 end fraction end cell end table  

Selanjutnya cari h to the power of negative 1 end exponent left parenthesis x right parenthesis. Misal h left parenthesis x right parenthesis equals y sehingga x equals h to the power of negative 1 end exponent left parenthesis y right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x plus 2 over denominator x minus 12 end fraction end cell row y equals cell fraction numerator 2 x plus 2 over denominator x minus 12 end fraction end cell row cell y left parenthesis x minus 12 right parenthesis end cell equals cell 2 x plus 2 end cell row cell y x minus 12 y end cell equals cell 2 x plus 2 end cell row cell y x minus 2 x end cell equals cell 2 plus 12 y end cell row cell left parenthesis y minus 2 right parenthesis x end cell equals cell 12 y plus 2 end cell row x equals cell fraction numerator 12 y plus 2 over denominator y minus 2 end fraction end cell row cell h to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 12 y plus 2 over denominator y minus 2 end fraction end cell row cell h to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 12 x plus 2 over denominator x minus 2 end fraction end cell end table 

Oleh karena itu, jawaban yang benar adalah C. 

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Roboguru

Diketahui fungsi  dan . Nilai 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 open parentheses fraction numerator x minus 1 over denominator 2 x plus 4 end fraction close parentheses minus 3 end cell row blank equals cell fraction numerator 4 x minus 4 over denominator 2 x plus 4 end fraction minus 3 end cell row blank equals cell fraction numerator 4 x minus 4 minus 6 x minus 12 over denominator 2 x plus 4 end fraction end cell row blank equals cell fraction numerator negative 2 x minus 16 over denominator 2 x plus 4 end fraction end cell row blank blank blank row y equals cell fraction numerator negative 2 x minus 16 over denominator 2 x plus 4 end fraction end cell row cell 2 x y plus 4 y end cell equals cell negative 2 x minus 16 end cell row cell 2 x y plus 2 x end cell equals cell negative 4 y minus 16 end cell row cell x left parenthesis 2 y plus 2 right parenthesis end cell equals cell negative 4 y minus 16 end cell row x equals cell fraction numerator negative 4 y minus 16 over denominator 2 y plus 2 end fraction end cell row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator negative 4 x minus 16 over denominator 2 x plus 2 end fraction end cell row blank blank blank row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 5 right parenthesis end cell equals cell fraction numerator negative 4 left parenthesis 5 right parenthesis minus 16 over denominator 2 left parenthesis 5 right parenthesis plus 2 end fraction end cell row blank equals cell fraction numerator negative 20 minus 16 over denominator 10 plus 2 end fraction end cell row blank equals cell fraction numerator negative 36 over denominator 12 end fraction end cell row blank equals cell negative 3 end cell end table end style

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Roboguru

Jika dan serta  maka nilai ....

Pembahasan Soal:

Jika dan   

kita cari lebih dahulu invers dari f(x)

 begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 10 y equals 2 x minus 10 y plus 10 equals 2 x fraction numerator y plus 10 over denominator 2 end fraction equals x f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 10 over denominator 2 end fraction end style

kemudian kita cari terlebih dahulu fungsi komposisinya :

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                begin mathsize 14px style equals f left parenthesis x plus p right parenthesis equals 2 left parenthesis x plus p right parenthesis minus 10 equals 2 x plus 2 p minus 10 end style

inversnya adalah :

begin mathsize 14px style y equals 2 x plus 2 p minus 10 y plus 10 minus 2 p equals 2 x fraction numerator y plus 10 minus 2 p over denominator 2 end fraction equals x open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 10 minus 2 p over denominator 2 end fraction end style

kita cari fungsi komposisi satunya:

begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g close parentheses left parenthesis x right parenthesis equals open parentheses f to the power of negative 1 end exponent left parenthesis g left parenthesis x right parenthesis right parenthesis close parentheses end style

                    begin mathsize 14px style equals open parentheses f to the power of negative 1 end exponent left parenthesis x plus p right parenthesis close parentheses equals fraction numerator x plus p plus 10 over denominator 2 end fraction end style

kita akan mencari nilai p dari persamaan:

begin mathsize 14px style fraction numerator x plus 10 minus 2 p over denominator 2 end fraction equals fraction numerator x plus p plus 10 over denominator 2 end fraction 10 minus 2 p equals p plus 10 minus 3 p equals 0 p equals 0 end style

maka nilai 0

jadi, jawabannya C

0

Roboguru

Diketahui fungsi ,  dan . Fungsi invers dari  adalah ....

Pembahasan Soal:

Fungsi invers

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator a x plus b over denominator c x plus d end fraction semicolon x not equal to negative d over c rightwards double arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative d x plus b over denominator c x minus a end fraction semicolon x not equal to a over c end style 

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 2 x minus 4 over denominator 5 minus x end fraction end stylebegin mathsize 14px style x not equal to 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 7 end style. Fungsi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell 3 open parentheses f open parentheses x close parentheses close parentheses plus 7 end cell row blank equals cell 3 open parentheses fraction numerator 2 x minus 4 over denominator 5 minus x end fraction close parentheses plus 7 end cell row blank equals cell fraction numerator 6 x minus 12 over denominator 5 minus x end fraction plus 7 end cell row blank equals cell fraction numerator 6 x minus 12 over denominator 5 minus x end fraction plus fraction numerator 7 open parentheses 5 minus x close parentheses over denominator 5 minus x end fraction end cell row blank equals cell fraction numerator 6 x minus 12 plus 35 minus 7 x over denominator 5 minus x end fraction end cell row blank equals cell fraction numerator negative x plus 23 over denominator negative x plus 5 end fraction end cell row blank blank blank row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 5 x plus 23 over denominator negative x plus 1 end fraction end cell end table end style 

Jadi, Error converting from MathML to accessible text.begin mathsize 14px style x not equal to 1 end style.

0

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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