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Jika dan , maka daerah definisi adalah ...

Jika begin mathsize 14px style straight f open parentheses straight x close parentheses equals square root of straight x plus 1 end root end style dan begin mathsize 14px style straight g open parentheses straight x close parentheses equals 2 straight x squared plus 4 end style, maka daerah definisi begin mathsize 14px style open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses end style adalah ...

  1. begin mathsize 14px style open curly brackets straight x element of straight real numbers close curly brackets end style 

  2. begin mathsize 14px style open curly brackets straight x greater or equal than 1 vertical line straight x element of straight real numbers close curly brackets end style 

  3. begin mathsize 14px style open curly brackets straight x not equal to negative 1 vertical line straight x element of straight real numbers close curly brackets end style 

  4. begin mathsize 14px style open curly brackets straight x greater or equal than negative 1 vertical line straight x element of straight real numbers close curly brackets end style 

  5. begin mathsize 14px style open curly brackets straight x not equal to 1 vertical line straight x element of straight real numbers close curly brackets end style 

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Pembahasan

Diketahui : dan , maka Sehingga kita dapatkan Karena terpenuhi (hasil dari pasti merupakan bilangan riil), maka

Diketahui : undefined dan undefined, maka 

begin mathsize 14px style straight D subscript straight f equals open curly brackets straight x greater or equal than negative 1 vertical line straight x element of straight real numbers close curly brackets straight D subscript straight g equals open curly brackets straight x element of straight real numbers close curly brackets end style

Sehingga kita dapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight D subscript straight g ring operator straight f end subscript end cell equals cell open curly brackets straight x element of straight D subscript straight f vertical line straight f open parentheses straight x close parentheses element of straight D subscript straight g close curly brackets end cell row blank equals cell open curly brackets straight x greater or equal than negative 1 vertical line straight f open parentheses straight x close parentheses element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets straight x greater or equal than negative 1 vertical line square root of straight x plus 1 end root element of straight real numbers close curly brackets end cell end table end style 

Karena begin mathsize 14px style square root of straight x plus 1 end root element of straight real numbers end style terpenuhi (hasil dari begin mathsize 14px style square root of straight x plus 1 end root end style pasti merupakan bilangan riil), maka

begin mathsize 14px style straight D subscript straight g ring operator straight f end subscript equals open curly brackets straight x greater or equal than negative 1 vertical line straight x element of straight real numbers close curly brackets end style 

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