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Diketahui  dengan daerah asal . Jika  daerah hasil...

Diketahui begin mathsize 14px style g left parenthesis x right parenthesis equals x plus 3 end style dengan daerah asal begin mathsize 14px style straight D subscript g equals left curly bracket x vertical line minus 5 less or equal than x less than 0 comma x element of straight R right curly bracket end style. Jika begin mathsize 14px style f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis squared end style daerah hasil begin mathsize 14px style y equals f left parenthesis x right parenthesis end style adalah ....

  1. begin mathsize 14px style left curly bracket y vertical line 0 less or equal than y less than 9 comma y element of straight R right curly bracket end style  

  2. undefined 

  3. begin mathsize 14px style left curly bracket y vertical line 0 less or equal than y less than 4 comma y element of straight R right curly bracket end style  

  4. begin mathsize 14px style open curly brackets y vertical line 0 less or equal than y less or equal than 4 comma y element of straight R close curly brackets end style 

  5. begin mathsize 14px style left curly bracket y vertical line 0 less than y less or equal than 4 comma y element of straight R right curly bracket end style 

Jawaban:

Fungsi adalah pemetaan setiap anggota sebuah himpunan daerah asal (domain) kepada anggota himpunan yang lain yang merupakan daerah kawan (kodomain).

Diketahui begin mathsize 14px style g left parenthesis x right parenthesis equals x plus 3 end style dengan daerah asal begin mathsize 14px style straight D subscript g equals left curly bracket x vertical line minus 5 less or equal than x less than 0 comma x element of straight R right curly bracket end style.

Untuk begin mathsize 14px style f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis squared end style diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell g left parenthesis x right parenthesis squared end cell row blank equals cell left parenthesis x plus 3 right parenthesis squared end cell row blank equals cell x squared plus 6 x plus 9 end cell end table 

Dengan domain begin mathsize 14px style f left parenthesis x right parenthesis end style sama dengan domain begin mathsize 14px style g left parenthesis x right parenthesis end style diperoleh:

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begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 4 right parenthesis end cell equals cell open parentheses negative 4 close parentheses squared plus 6 open parentheses negative 4 close parentheses plus 9 end cell row blank equals 1 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 3 right parenthesis end cell equals cell left parenthesis negative 3 right parenthesis squared plus 6 left parenthesis negative 3 right parenthesis plus 9 end cell row blank equals 0 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 2 right parenthesis end cell equals cell left parenthesis negative 2 right parenthesis squared plus 6 left parenthesis negative 2 right parenthesis plus 9 end cell row blank equals 1 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 1 right parenthesis end cell equals cell left parenthesis negative 1 right parenthesis squared plus 6 left parenthesis negative 1 right parenthesis plus 9 end cell row blank equals 4 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 0 close parentheses end cell equals cell 0 squared plus 6 open parentheses 0 close parentheses plus 9 end cell row blank equals 9 end table end style 

Diperoleh daerah hasil begin mathsize 14px style y equals f left parenthesis x right parenthesis end style untuk domain begin mathsize 14px style straight D subscript g equals left curly bracket x vertical line minus 5 less or equal than x less than 0 comma x element of straight R right curly bracket end style adalah  begin mathsize 14px style left curly bracket y vertical line 0 less or equal than y less than 9 comma y element of straight R right curly bracket end style.

Jadi jawaban yang tepat adalah A.

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