Roboguru

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

Pertanyaan

Diketahui fungsi f left parenthesis x right parenthesis equals 3 x plus 1 dan g left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator x plus 3 end fraction comma space x not equal to negative 3. Jika invers left parenthesis g ring operator f right parenthesis adalah left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent, nilai left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 2 right parenthesis equals....

  1. negative 3 over 4 

  2. 17 over 10 

  3. 5 over 2 

  4. 11 over 2 

  5. 15 over 2 

Pembahasan Soal:

Diketahui : f left parenthesis x right parenthesis equals 3 x plus 1g left parenthesis x right parenthesis equals fraction numerator 2 x minus 1 over denominator x plus 3 end fraction comma space x not equal to negative 3

Cari left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis terlebih dahulu

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 g left parenthesis left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g left parenthesis 3 x plus 1 right parenthesis end cell row blank equals cell fraction numerator 2 left parenthesis 3 x plus 1 right parenthesis minus 1 over denominator left parenthesis 3 x plus 1 right parenthesis plus 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 6 x plus 2 minus 1 over denominator 3 x plus 4 end fraction end cell row blank equals cell fraction numerator 6 x plus 1 over denominator 3 x plus 4 end fraction end cell end table 

Selanjutnya cari left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis. Misal left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals y, sehingga x equals left parenthesis g ring operator f right parenthesis 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 left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 6 x plus 1 over denominator 3 x plus 4 end fraction end cell row y equals cell fraction numerator 6 x plus 1 over denominator 3 x plus 4 end fraction end cell row cell y left parenthesis 3 x plus 4 right parenthesis end cell equals cell 6 x plus 1 end cell row cell 3 y x plus 4 y end cell equals cell 6 x plus 1 end cell row cell 3 y x minus 6 x end cell equals cell 1 minus 4 y end cell row cell x left parenthesis 3 y minus 6 right parenthesis end cell equals cell negative 4 y plus 1 end cell row x equals cell fraction numerator negative 4 y plus 1 over denominator 3 y minus 6 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 negative 4 y plus 1 over denominator 3 y minus 6 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 negative 4 x plus 1 over denominator 3 x minus 6 end fraction end cell end table   

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 2 right parenthesis end cell equals cell fraction numerator negative 4 left parenthesis negative 2 right parenthesis plus 1 over denominator 3 left parenthesis negative 2 right parenthesis minus 6 end fraction end cell row blank equals cell fraction numerator 8 plus 1 over denominator negative 6 minus 6 end fraction end cell row blank equals cell fraction numerator 9 over denominator negative 12 end fraction end cell row blank equals cell negative 3 over 4 end cell end table     

Oleh karena itu, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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