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Jika diketahui fungsi  dan . Daerah asal fungsi  a...

Jika diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 3 x plus 1 over denominator 2 x minus 1 end fraction comma space x not equal to 1 half comma space x element of R end style dan begin mathsize 14px style g open parentheses x close parentheses equals x plus 5 end style. Daerah asal fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style adalah ...  

  1. begin mathsize 14px style open curly brackets x vertical line x not equal to negative 4 comma space x element of R close curly brackets end style

         

  2. begin mathsize 14px style open curly brackets x vertical line x not equal to negative 9 over 2 comma space x element of R close curly brackets end style    

  3. begin mathsize 14px style open curly brackets x vertical line x not equal to negative 2 over 9 comma space x element of R close curly brackets end style    

  4. begin mathsize 14px style open curly brackets x vertical line x not equal to 2 over 9 comma space x element of R close curly brackets end style    

  5. begin mathsize 14px style open curly brackets x vertical line x not equal to 9 over 2 comma space x element of R close curly brackets end style    

Jawaban:

fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style dapat ditentukan dengan cara berikut

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses space space space space space space space space space space space space space equals f open parentheses x plus 5 close parentheses space space space space space space space space space space space space space equals fraction numerator 3 open parentheses x plus 5 close parentheses plus 1 over denominator 2 open parentheses x plus 5 close parentheses minus 1 end fraction space space space space space space space space space space space space equals fraction numerator 3 x plus 15 plus 1 over denominator 2 x plus 10 minus 1 end fraction space space space space space space space space space space space space equals fraction numerator 3 x plus 16 over denominator 2 x plus 9 end fraction end style 

Domain fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 9 end cell not equal to 0 row cell 2 x end cell not equal to cell negative 9 end cell row x not equal to cell negative 9 over 2 end cell end table end style 

begin mathsize 14px style D subscript open parentheses f ring operator g close parentheses end subscript equals open curly brackets x vertical line x not equal to negative 9 over 2 comma space x element of R close curly brackets end style 

Jadi,jawaban yang tepat adalah B

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