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Diketahui dan dengan dan . Agar terdefinisi, maka Dg​ dibatasi menjadi ....

Pertanyaan

Diketahui begin mathsize 14px style italic f open parentheses italic x close parentheses equals italic x squared minus sign 4 end styledan begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 1 end style dengan begin mathsize 14px style D subscript f equals open curly brackets x vertical line 1 less or equal than x less or equal than 3 comma x element of straight real numbers close curly brackets end style dan begin mathsize 14px style D subscript g equals open curly brackets x vertical line minus 2 less or equal than x less or equal than 2 comma x element of straight real numbers close curly brackets end style . Agar begin mathsize 14px style open parentheses f ring operator g close parentheses end style terdefinisi, maka begin mathsize 14px style D subscript g end style dibatasi menjadi ....

  1. Error converting from MathML to accessible text.

  2. begin mathsize 14px style open curly brackets x vertical line minus square root of 2 less or equal than x less or equal than square root of 2 comma x element of straight real numbers close curly brackets end style

  3. Error converting from MathML to accessible text.

  4. begin mathsize 14px style open curly brackets x vertical line minus square root of 2 less than x less than square root of 2 comma x element of straight real numbers close curly brackets end style

  5. begin mathsize 14px style open curly brackets x vertical line minus 2 less than x less than 2 comma x element of straight real numbers close curly brackets end style

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui undefined dengan undefined maka begin mathsize 14px style g open parentheses x close parentheses end style bisa kita gambarkan seperti berikut ini.

Sehingga begin mathsize 14px style R subscript g equals open curly brackets y vertical line 1 less or equal than y less or equal than 5 comma y element of straight real numbers close curly brackets end style  .

 

Selanjutnya, diketahui begin mathsize 14px style f open parentheses x close parentheses equals x squared minus 4 end style dengan undefined maka begin mathsize 14px style f open parentheses x close parentheses end style bisa kita gambarkan seperti berikut ini.

Sehingga begin mathsize 14px style R subscript f equals open curly brackets y vertical line minus 3 less or equal than y less or equal than 5 comma y element of straight real numbers close curly brackets end style

 

Perhatikan bahwa undefined dan undefined sehingga begin mathsize 14px style R subscript g ⊄ D subscript f end style karena begin mathsize 14px style 3 less than x less or equal than 5 end style bukan anggota begin mathsize 14px style D subscript f end style

Agar undefined Terdefinisi, kita batasi undefined dengan cara menghilangkan begin mathsize 14px style 3 less than x less or equal than 5 end style dari begin mathsize 14px style R subscript g end style sehingga begin mathsize 14px style R subscript g end style yang baru menjadi

begin mathsize 14px style R subscript g equals open curly brackets y vertical line 1 less or equal than y less or equal than 3 comma y element of straight real numbers close curly brackets end style 

 

Kita perlu mencari nilai x  yang mengakibatkan begin mathsize 14px style g open parentheses x close parentheses equals 3 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 5 end style

begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 1 3 equals x squared plus 1 x squared equals 2 x equals plus-or-minus square root of 2  g open parentheses x close parentheses equals x squared plus 1 5 equals x squared plus 1 x squared equals 4 x equals plus-or-minus 2 end style

Jadi, kita perlu menghilangkan begin mathsize 14px style negative 2 less or equal than x less than negative square root of 2 end style dan begin mathsize 14px style square root of 2 less or equal than x less than 2 end style  dari begin mathsize 14px style D subscript g end style sehingga begin mathsize 14px style D subscript g end style dibatasi menjadi begin mathsize 14px style D subscript g equals open curly brackets x vertical line minus square root of 2 less or equal than x less or equal than square root of 2 comma x element of straight real numbers close curly brackets end style

Jadi, jawaban yang tepat adalah B.

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