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Daerah hasil fungsi y=x2−2x−3 untuk daerah asal {x∣−1≤x≤4, x∈R} adalah ...

Pertanyaan

Daerah hasil fungsi begin mathsize 14px style y equals x squared minus 2 x minus 3 end style untuk daerah asal begin mathsize 14px style open curly brackets x vertical line minus 1 less or equal than x less or equal than 4 comma space x element of straight R close curly brackets end style adalah ... 

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

  2. begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than x less or equal than 11 comma space x element of straight R close curly brackets end style 

  3. begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than x less or equal than 5 comma space x element of straight R close curly brackets end style 

  4. begin mathsize 14px style open curly brackets y vertical line 0 less or equal than x less or equal than 5 comma space x element of straight R close curly brackets end style 

  5. begin mathsize 14px style open curly brackets y vertical line 0 less or equal than x less or equal than 11 comma space x element of straight R close curly brackets end style 

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

begin mathsize 14px style y equals x squared minus 2 x minus 3 end style dengan daerah asal begin mathsize 14px style open curly brackets x vertical line minus 1 less or equal than x less or equal than 4 comma space x element of straight R close curly brackets end style 

  • Uji batas interval domain, begin mathsize 14px style x equals negative 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell open parentheses negative 1 close parentheses squared minus 2 open parentheses negative 1 close parentheses minus 3 end cell row blank equals cell 1 plus 2 minus 3 end cell row blank equals 0 end table end style  

  • Uji batas interval domain, begin mathsize 14px style x equals 4 end style 

begin mathsize 14px style y equals 4 squared minus 2 open parentheses 4 close parentheses minus 3 equals 16 minus 8 minus 3 equals 5 end style 

  • Uji titik puncak

begin mathsize 14px style x equals negative fraction numerator b over denominator 2 a end fraction equals negative fraction numerator negative 2 over denominator 2 times 1 end fraction equals 1 end style 

            begin mathsize 14px style x equals 1 end style termasuk dalam domain, dengan nilai begin mathsize 14px style y end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 1 squared minus 2 open parentheses 1 close parentheses minus 3 end cell row blank equals cell 1 minus 2 minus 3 end cell row blank equals cell negative 4 end cell end table end style 

Perhatikan bahwa nilai minimum dari undefined adalah begin mathsize 14px style y equals negative 4 end style dan nilai maksimum undefined adalah begin mathsize 14px style y equals 5 end style. Sehingga daerah hasilnya adalah begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than y less or equal than 5 comma space y element of R close curly brackets end style

Jadi jawaban yang tepat adalah C.

2rb+

5.0 (4 rating)

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