Roboguru

Jika fungsi , , , dan , maka nilai  adalah ....

Pertanyaan

Jika fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus a end fraction end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus b end stylebegin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis 1 right parenthesis equals 1 half end style, dan begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis 1 right parenthesis equals 2 end style, maka nilai begin mathsize 14px style a b end style adalah ....

  1. begin mathsize 14px style 2 end style 

  2. begin mathsize 14px style 3 over 2 end style 

  3. begin mathsize 14px style 1 half end style 

  4. begin mathsize 14px style 0 end style 

  5. begin mathsize 14px style negative 1 end style 

Pembahasan Soal:

Penyelesaian soal tersebut adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses 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 fraction numerator 1 over denominator g left parenthesis x right parenthesis plus a end fraction end cell row blank equals cell fraction numerator 1 over denominator x squared plus b plus a end fraction end cell row cell open parentheses f ring operator g close parentheses left parenthesis 1 right parenthesis end cell equals cell 1 half end cell row cell fraction numerator 1 over denominator 1 plus b plus a end fraction end cell equals cell 1 half end cell row cell b plus a end cell equals cell 1 space.... left parenthesis 1 right parenthesis end cell end table end style  

Berikutnya,

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 g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell left parenthesis f left parenthesis x right parenthesis right parenthesis squared plus b space equals open parentheses fraction numerator 1 over denominator x plus a end fraction close parentheses squared plus b end cell row blank equals cell fraction numerator 1 over denominator x squared plus 2 a x plus a squared end fraction plus b end cell row blank equals cell fraction numerator 1 plus b open parentheses x squared plus 2 a x plus a squared close parentheses over denominator x squared plus 2 a x plus a squared end fraction end cell row cell left parenthesis g ring operator f right parenthesis left parenthesis 1 right parenthesis end cell equals 2 row cell fraction numerator 1 plus b plus 2 a b plus a squared b over denominator 1 plus 2 a plus a squared end fraction end cell equals 2 row cell a squared b plus 2 a b plus b plus 1 end cell equals cell 2 plus 4 a plus 2 a squared end cell row cell 2 a squared plus 4 a minus a squared b minus 2 a b minus b plus 1 end cell equals cell 0 space... left parenthesis 2 right parenthesis end cell row blank blank blank end table end style  

Subtitusi persamaan (1) ke persamaan (2):

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a squared plus 4 a minus a squared left parenthesis 1 minus a right parenthesis minus 2 a left parenthesis 1 minus a right parenthesis minus left parenthesis 1 minus b right parenthesis plus 1 end cell equals 0 row cell 2 a squared plus 4 a minus a squared plus a cubed minus 2 a plus 2 a squared minus 1 plus b plus 1 end cell equals 0 row cell a cubed plus 3 a squared plus 3 a end cell equals 0 row cell a left parenthesis a squared plus 3 a plus 3 right parenthesis end cell equals 0 row blank blank blank end table end style 

Salah satu nilai yang bernilai real adalah begin mathsize 14px style a equals 0 end style. Sehingga begin mathsize 14px style a b equals 0 end style.

Jadi, jawaban yang tepat adalah D.  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Februari 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved