Diketahui dan . Maka nilai adalah ....

Pertanyaan

Diketahui begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses equals negative straight x squared plus straight x minus 4 end style dan begin mathsize 14px style straight g open parentheses straight x close parentheses equals straight x minus 1 end style. Maka nilai begin mathsize 14px style straight f open parentheses negative 1 close parentheses end style adalah ....

  1. -10

  2. -6

  3. -4

  4. 0

  5. 4

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end cell equals cell negative straight x squared plus straight x minus 4 end cell row cell straight f open parentheses straight g open parentheses straight x close parentheses close parentheses end cell equals cell negative straight x squared plus straight x minus 4 end cell row cell straight f open parentheses straight x minus 1 close parentheses end cell equals cell negative straight x squared plus straight x minus 4 end cell end table end style

Untuk mencari undefined, kita misalkan begin mathsize 14px style straight x minus 1 equals straight a rightwards arrow straight x equals straight a plus 1 end style sehingga 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses straight x minus 1 close parentheses end cell equals cell negative straight x squared plus straight x minus 4 end cell row cell straight f open parentheses straight a close parentheses end cell equals cell negative open parentheses straight a plus 1 close parentheses squared plus open parentheses straight a plus 1 close parentheses minus 4 end cell row cell straight f open parentheses straight a close parentheses end cell equals cell negative open parentheses straight a squared plus 2 straight a plus 1 close parentheses plus straight a plus 1 minus 4 end cell row cell straight f open parentheses straight a close parentheses end cell equals cell negative straight a squared minus 2 straight a minus 1 plus straight a minus 3 end cell row cell straight f open parentheses straight a close parentheses end cell equals cell negative straight a squared minus straight a minus 4 end cell end table end style

Jadi

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

Perhatikan kita bisa mencarinya dengan cara berikut.

Kita dapatkan bahwa begin mathsize 14px style straight f open parentheses straight x minus 1 close parentheses equals negative straight x squared plus straight x minus 4 end style, maka undefined dipenuhi untuk 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x minus 1 end cell equals cell negative 1 end cell row straight x equals cell negative 1 plus 1 end cell row straight x equals 0 end table end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses 0 minus 1 close parentheses end cell equals cell negative open parentheses 0 close parentheses squared plus 0 minus 4 end cell row cell straight f open parentheses negative 1 close parentheses end cell equals cell 0 minus 4 end cell row cell straight f open parentheses negative 1 close parentheses end cell equals cell negative 4 end cell end table end style 

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