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Diketahui  dan . Daerah asal fungsi  adalah ...

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals x squared plus 8 x plus 12 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x minus 2 end style. Daerah asal fungsi begin mathsize 14px style open parentheses f over 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 2 comma space x element of straight real numbers close curly brackets end style

  2. begin mathsize 14px style left curly bracket x vertical line x not equal to negative 4 comma space x element of straight real numbers right curly bracket end style

  3. begin mathsize 14px style left curly bracket x vertical line x not equal to 2 comma space x element of straight real numbers right curly bracket end style

  4. begin mathsize 14px style open curly brackets x vertical line x not equal to negative 2 space dan space x not equal to negative 4 comma space x element of straight real numbers close curly brackets end style

  5. begin mathsize 14px style open curly brackets x vertical line x not equal to 2 space dan space x not equal to negative 4 comma space x element of straight real numbers close curly brackets end style

Jawaban:

Perhatikan perhitungan berikut ini.

Ingat, hasil bagi dua fungsi:

begin mathsize 14px style open parentheses f over g close parentheses open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f over g close parentheses left parenthesis x right parenthesis end cell equals cell fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator x squared plus 8 x plus 12 over denominator x minus 2 end fraction end cell end table end style

Perhatikan bahwa pada fungsi rasional begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p open parentheses x close parentheses over denominator q open parentheses x close parentheses end fraction end style, penyebut begin mathsize 14px style q open parentheses x close parentheses not equal to 0 end style, maka nilai undefined membuat penyebut sama dengan begin mathsize 14px style 0 end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals 0 row x equals 2 end table end style

Didapatkan nilai begin mathsize 14px style x equals 2 end style membuat penyebut sama dengan begin mathsize 14px style 0 end style maka begin mathsize 14px style x not equal to 2 end style.

Jadi, daerah asal fungsi begin mathsize 14px style open parentheses f over g close parentheses open parentheses x close parentheses end style adalah begin mathsize 14px style left curly bracket x vertical line x not equal to 2 comma space x element of straight real numbers right curly bracket end style.

Dengan demikian, jawaban yang tepat adalah C.

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