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Diketahui  dan , maka  adalah...

Pertanyaan

Diketahui f open parentheses x close parentheses equals x plus 3 dan g open parentheses x close parentheses equals fraction numerator x minus 1 over denominator x end fraction comma space x not equal to 0, maka open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses adalah...

  1. fraction numerator 2 plus 3 x over denominator x minus 1 end fraction

  2. fraction numerator 2 minus 3 x over denominator x plus 1 end fraction

  3. fraction numerator 2 minus 3 x over denominator x minus 1 end fraction

  4. fraction numerator 3 x plus 2 over denominator x plus 1 end fraction

  5. fraction numerator 3 x minus 2 over denominator 1 plus x end fraction

Pembahasan Soal:

Dengan menggunakan konsep komposisi fungsi diperoleh

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 g open parentheses x plus 3 close parentheses end cell row blank equals cell fraction numerator x plus 3 minus 1 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator x plus 2 over denominator x plus 3 end fraction end cell end table

Selanjutnya dengan menggunakan konsep invers fungsi diperoleh

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 y row cell fraction numerator x plus 2 over denominator x plus 3 end fraction end cell equals y row cell x plus 2 end cell equals cell y open parentheses x plus 3 close parentheses end cell row cell x plus 2 end cell equals cell x y plus 3 y end cell row cell x minus x y end cell equals cell 3 y minus 2 end cell row cell x open parentheses 1 minus y close parentheses end cell equals cell 3 y minus 2 end cell row x equals cell fraction numerator 3 y minus 2 over denominator 1 minus y 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 3 x minus 2 over denominator 1 minus x end fraction end cell row blank equals cell fraction numerator 2 minus 3 x over denominator x minus 1 end fraction end cell end table

Dengan demikian Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Nur

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika fungsi  dan g(x) = 3x + 1 maka = ....

Pembahasan Soal:

begin mathsize 14px style straight i right parenthesis space Cari space straight g ring operator straight f  space space space open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals 3 straight f open parentheses straight x close parentheses plus 1 equals 3. fraction numerator 2 straight x plus 3 over denominator straight x minus 5 end fraction plus 1 equals fraction numerator 6 straight x plus 9 over denominator straight x minus 5 end fraction plus fraction numerator straight x minus 5 over denominator straight x minus 5 end fraction  space space space equals fraction numerator 6 straight x plus 9 plus straight x minus 5 over denominator straight x minus 5 end fraction equals fraction numerator 7 straight x plus 4 over denominator straight x minus 5 end fraction    ii right parenthesis space Cari space invers space dengan space formula space berikut  space space space space straight h open parentheses straight x close parentheses equals fraction numerator ax plus straight b over denominator cx plus straight d end fraction rightwards arrow straight h to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction    space space space space open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals fraction numerator 7 straight x plus 4 over denominator straight x minus 5 end fraction  space space space space Dengan space straight a equals 7 comma space straight b equals 4 comma space straight c equals 1 comma space straight d equals negative 5 comma space maka  space space space space open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 5 straight x plus 4 over denominator straight x minus 7 end fraction end style

0

Roboguru

Jika  dan , tentukan: c.

Pembahasan Soal:

Diketahui:

 begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 4 end style 

begin mathsize 14px style g open parentheses x close parentheses equals 3 x plus 9 end style

Ditanyakan:

 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 adalah...

jawab:

pertama kita menentukan fungsi komposisi:

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 open parentheses g open parentheses x close parentheses close parentheses end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses 3 x plus 9 close parentheses end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 2 left parenthesis 3 x plus 9 right parenthesis minus 4 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 6 x plus 18 minus 4 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 6 x plus 14 end cell end table end style

Kemudian kita tentukan fungsi invers dari fungsi komposisi tersebut:

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 equals 6 x plus 14 y equals 6 x plus 14 6 x equals y minus 14 x equals fraction numerator y minus 14 over denominator 6 end fraction end cell 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 equals fraction numerator x minus 14 over denominator 6 end fraction end cell end table end style

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 x minus 14 over denominator 6 end fraction end cell end table end style

0

Roboguru

Diketahui   dan . Jika   Tentukan nilai dari !

Pembahasan Soal:

Ingat: konsep komposisi dua fungsi begin mathsize 14px style f ring operator g open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style 

Diketahui: undefined , undefined dan 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 equals 0 end style 
Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g 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 open parentheses x minus 1 close parentheses end cell row blank equals cell fraction numerator 1 over denominator x minus 1 end fraction end cell end table end style 

begin mathsize 14px style Misal colon space y equals f ring operator g left parenthesis x right parenthesis end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 1 over denominator x minus 1 end fraction end cell row cell x y minus y end cell equals 1 row cell x y end cell equals cell 1 plus y end cell row x equals cell fraction numerator 1 plus y over denominator y end fraction end cell end table end style 

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

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes 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 0 row cell fraction numerator 1 plus x over denominator x end fraction end cell equals 0 row cell 1 plus x end cell equals 0 row x equals cell negative 1 end cell end table end style   

Jadi, nilai begin mathsize 14px style bold italic x bold equals bold minus bold 1 end style

0

Roboguru

Jika  dan , untuk , maka daerah asal dari  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g left parenthesis x right parenthesis end cell equals cell f left parenthesis x squared right parenthesis end cell row cell f ring operator g left parenthesis x right parenthesis end cell equals cell fraction numerator 6 over denominator x squared plus 3 end fraction end cell row cell x squared plus 3 end cell equals cell fraction numerator 6 over denominator f ring operator g left parenthesis x right parenthesis end fraction end cell row cell x squared end cell equals cell fraction numerator 6 over denominator f ring operator g left parenthesis x right parenthesis end fraction minus 3 end cell row x equals cell square root of open parentheses fraction numerator 6 over denominator f ring operator g left parenthesis x right parenthesis end fraction minus 3 close parentheses end root end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell square root of 6 over x minus 3 end root end cell row blank blank blank row blank blank blank end table end style

Domain atau daerah asal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 over x minus 3 end cell greater or equal than 0 row cell fraction numerator 6 minus 3 x over denominator x end fraction end cell greater or equal than 0 row 0 less than cell x less than 2 end cell end table end style

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diketahui fungsi  dan . Tentukan : a.

Pembahasan Soal:

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis y equals f open parentheses g open parentheses x close parentheses close parentheses y equals 2 left parenthesis g left parenthesis x right parenthesis right parenthesis plus 1 y equals 2 left parenthesis x plus 3 right parenthesis plus 1 y equals 2 x plus 7 2 x equals y minus 7 x equals fraction numerator y minus 7 over denominator 2 end fraction left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 7 over denominator 2 end fraction end style

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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