Roboguru

Diketahui fungsi  dan . Jika  daerah asal fungsi  ...

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 4 over denominator x minus 5 end fraction end style dan begin mathsize 14px style g open parentheses x close parentheses equals square root of x squared minus 9 x end root end style. Jika begin mathsize 14px style h open parentheses x close parentheses equals open parentheses f times g close parentheses open parentheses x. close parentheses end style daerah asal fungsi begin mathsize 14px style h open parentheses x close parentheses end style adalah ...  

  1. begin mathsize 14px style open curly brackets x vertical line x not equal to 5 comma space x element of R close curly brackets end style      

  2. begin mathsize 14px style open curly brackets x vertical line x greater or equal than 0 comma space x not equal to 5 comma space x element of R close curly brackets end style    

  3. begin mathsize 14px style open curly brackets x vertical line x less or equal than 5 space atau space x greater or equal than 9 comma space x element of R close curly brackets end style    

  4.   begin mathsize 14px style open curly brackets x vertical line x less or equal than 0 space atau space x greater or equal than 9 comma space x element of R close curly brackets end style  

  5. begin mathsize 14px style open curly brackets x vertical line x less or equal than negative 9 space atau space x greater or equal than 9 comma space x element of R close curly brackets end style    

Jawaban:

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 4 over denominator x minus 5 end fraction end style

Daerah asal begin mathsize 14px style f open parentheses x close parentheses end style adalah 

begin mathsize 14px style D subscript f colon space x minus 5 not equal to 0 space space space space space space x not equal to 5 end style 

begin mathsize 14px style g open parentheses x close parentheses equals square root of x squared minus 9 x end root end style

Daerah asal begin mathsize 14px style g open parentheses x close parentheses end style adalah

 begin mathsize 14px style D subscript g colon space space space x squared minus 9 x greater or equal than 0 space space space space space space space space x open parentheses x minus 9 close parentheses greater or equal than 0 space space space space space space space space x equals 0 space atau space straight x equals 9 end style  

garis bilangannya

begin mathsize 14px style D g colon space x less or equal than 0 space atau space x greater or equal than 0 end style 

Domain dari begin mathsize 14px style h open parentheses x close parentheses equals open parentheses f times g close parentheses open parentheses x. close parentheses end style adalah 

begin mathsize 14px style D subscript f intersection D subscript g equals open curly brackets x not equal to 5 close curly brackets intersection open curly brackets x less or equal than 0 space atau space straight x greater or equal than 9 close curly brackets space space space space space space space space space space space space equals open curly brackets x vertical line x less or equal than 0 space atau space straight x greater or equal than 9 comma space x element of R close curly brackets end style  

Jadi, jawaban yang tepat adalah D

0

Ruangguru

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