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

Pembahasan Soal:

Diketahui f open parentheses x close parentheses equals 1 over x dan g open parentheses x close parentheses equals 2 x minus 1, maka diperoleh fungsi komposisi open parentheses f ring operator g close parentheses open parentheses x close parentheses sebagai berikut.

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

Kemudian, invers fungsi open parentheses f ring operator g close parentheses open parentheses x close parentheses sebagai berikut.

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


Dengan demikian, open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 1 plus x over denominator 2 x end fraction comma space x not equal to 0.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 07 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Fungsi  ditentukan oleh  .  Tentukan :

Pembahasan Soal:

pertama-tama, tentukan fungsi 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 cell left parenthesis f ring operator g right parenthesis end cell equals cell 2 left parenthesis 3 x plus 5 right parenthesis minus 1 end cell row blank equals cell 6 x plus 9 end cell end table end style

setelah itu, tentukan fungsi inversnya.

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 6 x plus 9 end cell row y equals cell 6 x plus 9 end cell row x equals cell fraction numerator y minus 9 over denominator 6 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 x minus 9 over denominator 6 end fraction end cell end table end style

Dengan begitu, dapat diperoleh nilai dari begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 1 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 to the power of negative 1 end exponent left parenthesis 1 right parenthesis end cell equals cell fraction numerator 1 minus 9 over denominator 6 end fraction end cell row blank equals cell negative 4 over 3 end cell end table end style

0

Roboguru

Diketahui fungsi  dan . Invers  adalah ....

Pembahasan Soal:

Dengan menerapkan konsep komposisi fungsi:

Error converting from MathML to accessible text. 

Dengan konsep invers fungsi:

Error converting from MathML to accessible text. 

Misalkan begin mathsize 14px style straight y equals left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell fraction numerator 12 straight x minus 15 over denominator 2 straight x plus 1 end fraction plus 4 end cell row cell straight y minus 4 end cell equals cell fraction numerator 12 straight x minus 15 over denominator 12 straight x plus 1 end fraction end cell row cell left parenthesis straight y minus 4 right parenthesis left parenthesis 2 straight x plus 1 right parenthesis end cell equals cell 2 straight x minus 15 end cell row cell 2 yx plus straight y minus 8 straight x minus 4 end cell equals cell 12 straight x minus 15 end cell row cell 2 yx minus 8 straight x minus 12 straight x end cell equals cell negative 15 minus straight y plus 4 end cell row cell 2 yx minus 20 straight x end cell equals cell negative 15 minus straight y plus 4 end cell row cell straight x left parenthesis 2 straight y minus 20 right parenthesis end cell equals cell negative 11 minus straight y end cell row straight x equals cell fraction numerator negative left parenthesis straight y plus 11 right parenthesis over denominator 2 straight y minus 20 end fraction end cell row straight x equals cell fraction numerator left parenthesis straight y plus 11 right parenthesis over denominator negative left parenthesis 2 straight y minus 20 right parenthesis end fraction end cell row straight x equals cell fraction numerator straight y plus 11 over denominator negative 2 straight y plus 20 end fraction end cell row cell straight f to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell equals cell fraction numerator straight y plus 11 over denominator negative 2 straight y plus 20 end fraction end cell row cell left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell fraction numerator straight x plus 11 over denominator negative 2 straight x plus 20 end fraction end cell row cell left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell fraction numerator straight x plus 11 over denominator negative 2 straight x plus 20 end fraction end cell end table end style  

Jadi, Jika begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 3 straight x plus 4 end style dan begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals fraction numerator 4 straight x minus 5 over denominator 2 straight x plus 1 end fraction comma space straight x not equal to negative 1 half end style, maka Error converting from MathML to accessible text..

Oleh karena itu, Jawaban yang benar adalah D

0

Roboguru

Jika diketahui bahwa f (x) = 2x, g(x) = 3 - 5x,

Pembahasan Soal:

f left parenthesis x right parenthesis equals 2 x  g left parenthesis x right parenthesis equals 3 minus 5 x  left parenthesis g o f right parenthesis left parenthesis x right parenthesis equals 3 minus 5 left parenthesis 2 x right parenthesis  left parenthesis g o f right parenthesis left parenthesis x right parenthesis equals 3 minus 10 x  left parenthesis g o f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals 3 minus 10 x  y equals 3 minus 10 x  10 x equals 3 minus y  x equals fraction numerator 3 minus y over denominator 10 end fraction  y equals 1 over 10 left parenthesis 3 minus x right parenthesis

0

Roboguru

Diketahui fungsi   dan . Fungsi invers dari  adalah ...

Pembahasan Soal:

 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 3 x plus 1 close parentheses end cell row cell space space space space space space space space space space space space space end cell equals cell fraction numerator 2 open parentheses 3 x plus 1 close parentheses over denominator open parentheses 3 x plus 1 close parentheses plus 3 end fraction end cell row cell space space space space space space space space space space space space space end cell equals cell fraction numerator 6 x plus 2 over denominator 3 x plus 4 end fraction end cell row cell m i s a l space y end cell equals cell fraction numerator 6 x plus 2 over denominator 3 x plus 4 end fraction end cell row cell y open parentheses 3 x plus 4 close parentheses end cell equals cell 6 x plus 2 end cell row cell 3 x y plus 4 y space end cell equals cell 6 x plus 2 end cell row cell 3 x y minus 6 x space end cell equals cell 2 minus 4 y end cell row cell x open parentheses 3 y minus 6 close parentheses end cell equals cell 2 minus 4 y end cell row x equals cell fraction numerator 2 minus 4 y over denominator 3 y minus 6 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 2 minus 4 x over denominator 3 x minus 6 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses end cell equals cell fraction numerator 2 minus 4 open parentheses negative 2 close parentheses over denominator 3 open parentheses negative 2 close parentheses minus 6 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell fraction numerator 2 plus 8 over denominator negative 6 minus 6 end fraction end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell negative 10 over 12 end cell row cell space space space space space space space space space space space space space space space space space space space end cell equals cell negative 5 over 6 end cell row blank blank blank end table end style  

0

Roboguru

Diketahui dan . Nilai ....

Pembahasan Soal:

Diketahui dan .

kita cari dlu fungsi komposisinya :

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis end style

                begin mathsize 14px style equals g open parentheses 5 x plus 1 half close parentheses equals 3 over 4 open parentheses 5 x plus 1 half close parentheses minus 6 equals 15 over 4 x plus 3 over 8 minus 6 equals 15 over 4 x minus 45 over 8 end style

kemudian kita tentukan inversnya :

begin mathsize 14px style y equals 15 over 4 x minus 45 over 8 8 y equals 30 x minus 45 8 y plus 45 equals 30 x fraction numerator 8 y plus 45 over denominator 30 end fraction equals x open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 8 x plus 45 over denominator 30 end fraction  left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 5 right parenthesis equals fraction numerator 8 open parentheses negative 5 close parentheses plus 45 over denominator 30 end fraction equals fraction numerator negative 40 plus 45 over denominator 30 end fraction equals 5 over 30 equals 1 over 6 end style

jadi, jawabannya E

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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