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Pertanyaan

Jika f open parentheses x close parentheses equals x minus 2 dan g open parentheses x close parentheses equals x plus 4 maka open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals.... 

  1. x minus 4 

  2. x minus 2 

  3. x 

  4. x plus 2 

  5. x plus 4 

Pembahasan Soal:

Tentukan fungsi komposisinya.

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 f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses x plus 4 close parentheses end cell row blank equals cell x plus 4 minus 2 end cell row blank equals cell x plus 2 end cell end table 

Tentukan inversnya.

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 y row cell x plus 2 end cell equals y row x equals cell y minus 2 end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell y minus 2 end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell x minus 2 end cell end table 

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Nur

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Diketahui fungsi  dengan , maka  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 f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f left parenthesis 2 x minus 1 right parenthesis end cell row blank equals cell fraction numerator left parenthesis 2 x minus 1 right parenthesis plus 4 over denominator left parenthesis 2 x minus 1 right parenthesis minus 6 end fraction end cell row blank equals cell fraction numerator 2 x plus 3 over denominator 2 x minus 7 end fraction end cell row y equals cell fraction numerator 2 x plus 3 over denominator 2 x minus 7 end fraction end cell row cell y times left parenthesis 2 x minus 7 right parenthesis end cell equals cell 2 x plus 3 end cell row cell 2 x y minus 7 y end cell equals cell 2 x plus 3 end cell row cell 2 x y minus 2 end cell equals cell 7 y plus 3 end cell row cell x times left parenthesis 2 y minus 2 right parenthesis end cell equals cell 7 y plus 3 end cell row x equals cell fraction numerator 7 y plus 3 over denominator 2 y minus 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 7 x plus 3 over denominator 2 x minus 2 end fraction space. end cell end table end style

0

Roboguru

Diketahui fungsi . Invers  adalah ...

Pembahasan Soal:

Diketahui:

f left parenthesis x right parenthesis equals 3 x plus 4 space dan space g left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 1 end fraction semicolon space x not equal to negative 1 half

Mencari left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses ring operator g open parentheses x close parentheses end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f open parentheses fraction numerator 4 x minus 5 over denominator 2 x plus 1 end fraction close parentheses end cell row blank equals cell 3 open parentheses fraction numerator 4 x minus 5 over denominator 2 x plus 1 end fraction close parentheses plus 4 end cell row blank equals cell fraction numerator 12 x minus 15 over denominator 2 x plus 1 end fraction plus 4 end cell row blank equals cell fraction numerator 12 x minus 15 over denominator 2 x plus 1 end fraction plus fraction numerator 4 open parentheses 2 x plus 1 close parentheses over denominator 2 x plus 1 end fraction end cell row blank equals cell fraction numerator 12 x minus 15 plus 4 open parentheses 2 x plus 1 close parentheses over denominator 2 x plus 1 end fraction end cell row blank equals cell fraction numerator 20 x minus 11 over denominator 2 x plus 1 end fraction end cell end table 

Mencari invers dari left parenthesis f ring operator g right parenthesis 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 20 x minus 11 over denominator 2 x plus 1 end fraction end cell row y equals cell fraction numerator 20 x minus 11 over denominator 2 x plus 1 end fraction end cell row x equals cell fraction numerator 20 y minus 11 over denominator 2 y plus 1 end fraction end cell row cell x open parentheses 2 y plus 1 close parentheses end cell equals cell 20 y minus 11 end cell row cell 2 y x plus x minus x end cell equals cell 20 y minus 11 minus x end cell row cell 2 y x minus 20 y end cell equals cell 20 y minus 11 minus x minus 20 y end cell row cell 2 y x minus 20 y end cell equals cell negative 11 minus x end cell row cell 2 y x minus 20 y end cell equals cell negative 11 minus x end cell row cell fraction numerator 2 y open parentheses x minus 10 close parentheses over denominator 2 open parentheses x minus 10 close parentheses end fraction end cell equals cell negative fraction numerator 11 over denominator 2 open parentheses x minus 10 close parentheses end fraction minus fraction numerator x over denominator 2 open parentheses x minus 10 close parentheses end fraction end cell row y equals cell fraction numerator negative 11 minus x over denominator 2 open parentheses negative 10 plus x close parentheses end fraction comma space x not equal to 10 end cell row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis to the power of negative 1 end exponent end cell equals cell fraction numerator negative 11 minus x over denominator 2 open parentheses negative 10 plus x close parentheses end fraction comma space x not equal to 10 end cell row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis to the power of negative 1 end exponent end cell equals cell fraction numerator x plus 11 over denominator negative 2 x plus 20 end fraction comma space x not equal to 10 end cell end table 

Jadi, 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 11 over denominator negative 2 x plus 20 end fraction semicolon space x not equal to 10.

Dengan demikian, jawaban yang tepat adalah B.

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Roboguru

Jika dan , maka ....

Pembahasan Soal:

untuk mencari size 14px f to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis x right parenthesis end style, maka kita harus mencari f(x) terlebih dahulu dengan cara :

open parentheses f ring operator g ring operator g to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis equals open parentheses f ring operator I close parentheses left parenthesis x right parenthesis equals f left parenthesis x right parenthesis 

maka kita harus cari dulu begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis end style,

begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x plus 3 y equals 2 x plus 3 y minus 3 equals 2 x fraction numerator y minus 3 over denominator 2 end fraction equals x g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 3 over denominator 2 end fraction end style

kemudian kita komposisikan dengan , maka :

begin mathsize 14px style open parentheses f ring operator g ring operator g to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis equals open parentheses f ring operator g close parentheses left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis space space space space space space space space space space space space space space space space space space space space space space equals open parentheses f ring operator g close parentheses open parentheses fraction numerator x minus 3 over denominator 2 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space equals 2 open parentheses fraction numerator x minus 3 over denominator 2 end fraction close parentheses plus 5 space space space space space space space space space space space space space space space space space space space space space space space equals x minus 3 plus 5 space space space space space space space space space space space space space space space space space space space space space space space equals x plus 2 end style

kita cari inversnya :

y = x + 2

y - 2 = x

size 14px f to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis x right parenthesis end style = x - 2

Jadi jawabannya B

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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.

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Roboguru

Diketahui fungsi . Jika invers fungsi  dan invers fungsi . Tentukan:

Pembahasan Soal:

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 1 space dan space g left parenthesis x right parenthesis equals fraction numerator x minus 4 over denominator 6 x end fraction comma x not equal to 0 end style

Menentukan begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell row blank equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f left parenthesis fraction numerator x minus 4 over denominator 6 x end fraction right parenthesis end cell row blank equals cell 2 left parenthesis fraction numerator x minus 4 over denominator 6 x end fraction right parenthesis minus 1 end cell row blank equals cell fraction numerator 2 x minus 8 over denominator 6 x end fraction minus fraction numerator 6 x over denominator 6 x end fraction end cell row blank equals cell fraction numerator 2 x minus 8 minus 6 x over denominator 6 x end fraction end cell row blank equals cell fraction numerator negative 4 x minus 8 over denominator 6 x end fraction end cell row blank equals cell fraction numerator 2 left parenthesis negative 2 x minus 4 right parenthesis over denominator 6 x end fraction end cell row blank equals cell fraction numerator negative 2 x minus 4 over denominator 3 x end fraction comma x not equal to 0 end cell end table end style 

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

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 fraction numerator negative 2 x minus 4 over denominator 3 x end fraction end cell row y equals cell fraction numerator negative 2 x minus 4 over denominator 3 x end fraction end cell row cell 3 x y end cell equals cell negative 2 x minus 4 end cell row cell 3 x y plus 2 x end cell equals cell negative 4 end cell row cell x left parenthesis 3 y plus 2 right parenthesis end cell equals cell negative 4 end cell row x equals cell fraction numerator negative 4 over denominator 3 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 y right parenthesis end cell equals cell fraction numerator negative 4 over denominator 3 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 over denominator 3 x plus 2 end fraction comma x not equal to fraction numerator negative 2 over denominator 3 end fraction end cell end table end style 

a. Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f ring operator g right parenthesis 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 negative 4 over denominator 3 x plus 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 2 over denominator 3 end fraction end cell end table end style.

Menentukan begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis 2 x minus 1 right parenthesis end cell row blank equals cell fraction numerator 2 x minus 1 minus 4 over denominator 6 left parenthesis 2 x minus 1 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction comma space x not equal to 1 half end cell end table end style 

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

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction end cell row y equals cell fraction numerator 2 x minus 5 over denominator 12 x minus 6 end fraction end cell row cell y left parenthesis 12 x minus 6 right parenthesis end cell equals cell 2 x minus 5 end cell row cell 12 x y minus 6 y end cell equals cell 2 x minus 5 end cell row cell 12 x y minus 2 x end cell equals cell 6 y minus 5 end cell row cell x left parenthesis 12 y minus 2 right parenthesis end cell equals cell 6 y minus 5 end cell row x equals cell fraction numerator 6 y minus 5 over denominator 12 y minus 2 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 6 y minus 5 over denominator 12 y minus 2 end fraction end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 6 x minus 5 over denominator 12 x minus 2 end fraction comma space x not equal to 1 over 6 end cell row blank blank blank row blank blank blank end table end style 

b. Jadi, begin mathsize 14px style left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 6 x minus 5 over denominator 12 x minus 2 end fraction comma x not equal to 1 over 6 end style

 

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