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Diketahui dan   dengan dan . Domain f∘g adalah ....

Pertanyaan

Diketahuibegin mathsize 14px style f open parentheses x close parentheses equals x squared minus 3 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 2 x squared end style  dengan begin mathsize 14px style D subscript f 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 dan begin mathsize 14px style D subscript g equals open curly brackets x vertical line minus 1 less or equal than x less or equal than 1 comma x element of straight real numbers close curly brackets end style . Domain begin mathsize 14px style f ring operator g end style adalah ....

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

  2. begin mathsize 14px style open curly brackets x vertical line minus 1 less than x less than 1 comma x element of straight real numbers close curly brackets end style

  3. begin mathsize 14px style 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

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

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Jawaban terverifikasi

Jawaban

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

Pembahasan

Diketahui begin mathsize 14px style g open parentheses x close parentheses equals 2 x squared end style dengan begin mathsize 14px style D subscript g equals open curly brackets x vertical line minus 1 less or equal than x less or equal than 1 comma x element of straight real numbers close curly brackets end style , maka begin mathsize 14px style g left parenthesis x right parenthesis end style bisa kita gambarkan seperti berikut ini.

Sehingga begin mathsize 14px style R subscript g equals open curly brackets y vertical line 0 less or equal than y less or equal than 2 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 3 end style dengan begin mathsize 14px style D subscript f 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 , maka begin mathsize 14px style f left parenthesis x right parenthesis 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 1 comma y element of straight real numbers close curly brackets end style

 

Perhatikan bahwa begin mathsize 14px style R subscript g equals open curly brackets y vertical line 0 less or equal than y less or equal than 2 comma y element of straight real numbers close curly brackets end style dan begin mathsize 14px style D subscript f 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  sehingga begin mathsize 14px style R subscript g subset of D subscript f end style .

Oleh karena itu, begin mathsize 14px style f ring operator g end style terdefinisi sehingga  begin mathsize 14px style D subscript f ring operator g end subscript equals D subscript g equals open curly brackets x vertical line minus 1 less or equal than x less or equal than 1 comma x element of straight real numbers close curly brackets end style

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