Iklan

Pertanyaan

Diketahui : ( g − 1 ∘ f − 1 ) ( x ) f − 1 ( x ) ​ = = ​ x − 2 x ​ 2 x ​ Tentukan : g ( x ) = ... ? Catatan : ( g − 1 ∘ f − 1 ) ( x ) = ( f ∘ g ) − 1 ( x )

Diketahui :  

Tentukan : 

Catatan :   

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

00

:

17

:

10

:

15

Iklan

K. Prameswari

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh

diperoleh g open parentheses x close parentheses equals fraction numerator 4 x over denominator x minus 1 end fraction 

Pembahasan

Perhatikan bahwa Misalkan . Maka dapat diperoleh Selanjutnyadimisalkan , maka didapat Jadi, diperoleh

Perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell row cell fraction numerator x over denominator x minus 2 end fraction end cell equals cell g to the power of negative 1 end exponent open parentheses 2 x close parentheses end cell end table

Misalkan y equals 2 x space left right arrow y over 2 equals x. Maka dapat diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x over denominator x minus 2 end fraction end cell equals cell g to the power of negative 1 end exponent open parentheses 2 x close parentheses end cell row cell fraction numerator begin display style y over 2 end style over denominator begin display style y over 2 end style minus 2 end fraction end cell equals cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell row cell fraction numerator begin display style y over 2 end style over denominator begin display style fraction numerator y minus 4 over denominator 2 end fraction end style end fraction end cell equals cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell row cell fraction numerator y over denominator y minus 4 end fraction end cell equals cell g to the power of negative 1 end exponent open parentheses y close parentheses space left right arrow space g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x over denominator x minus 4 end fraction end cell end table 

Selanjutnya dimisalkan z equals g to the power of negative 1 end exponent open parentheses x close parentheses, maka didapat

table attributes columnalign right center left columnspacing 0px end attributes row z equals cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell row z equals cell fraction numerator x over denominator x minus 4 end fraction end cell row cell z open parentheses x minus 4 close parentheses end cell equals x row cell z x minus 4 z end cell equals x row cell z x minus x end cell equals cell 4 z end cell row cell x left parenthesis z minus 1 right parenthesis end cell equals cell 4 z end cell row x equals cell fraction numerator 4 z over denominator z minus 1 end fraction end cell row cell g open parentheses z close parentheses end cell equals cell fraction numerator 4 z over denominator z minus 1 end fraction space left right arrow space g open parentheses x close parentheses equals fraction numerator 4 x over denominator x minus 1 end fraction end cell end table 

Jadi, diperoleh g open parentheses x close parentheses equals fraction numerator 4 x over denominator x minus 1 end fraction 

Buka akses jawaban yang telah terverifikasi

lock

Yah, akses pembahasan gratismu habis


atau

Dapatkan jawaban pertanyaanmu di AiRIS. Langsung dijawab oleh bestie pintar

Tanya Sekarang

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

4

Diana Yukhafida Pebiola

Diana Yukhafida Pebiola

Bantu banget Makasih ❤️

Iklan

Roboguru Plus

Dapatkan pembahasan soal ga pake lama, langsung dari Tutor!

Tanya ke Forum

Biar Robosquad lain yang jawab soal kamu