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Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals negative 3 x squared plus 4 x plus 21 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared minus 7 x minus 10 end style. Rumus fungsi begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end style dan nilai begin mathsize 14px style f left parenthesis negative 2 right parenthesis plus g left parenthesis 3 right parenthesis minus left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end style adalah ....

  1. begin mathsize 14px style 4 x squared plus 11 x plus 31 blank dan space minus 45 end style 

  2. begin mathsize 14px style 2 x squared plus 11 x plus 31 space dan space minus 43 end style ​​​ ​​​

  3. begin mathsize 14px style negative 2 x squared plus 11 x plus 31 space dan space minus 39 end style ​  ​​​

  4. begin mathsize 14px style negative 4 x squared plus 11 x plus 31 space dan space 7 end style 

  5. begin mathsize 14px style negative 4 x squared plus 11 x plus 31 space dan space minus 37 end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Pertama kita cari rumus fungsi untuk begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end style, didapat

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis end cell row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell left parenthesis negative 3 x squared plus 4 x plus 21 right parenthesis minus left parenthesis x squared minus 7 x minus 10 right parenthesis end cell row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 3 x squared plus 4 x plus 21 minus x squared plus 7 x plus 10 end cell row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 3 x squared minus x squared plus 4 x plus 7 x plus 21 plus 10 end cell row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 4 x squared plus 11 x plus 31 end cell end table end style 

Selanjutnya, mencari masing-masing nilai begin mathsize 14px style f left parenthesis negative 2 right parenthesis end stylebegin mathsize 14px style g left parenthesis 3 right parenthesis end style, dan begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell negative 3 x squared plus 4 x plus 21 blank end cell row cell f open parentheses negative 2 close parentheses end cell equals cell negative 3 open parentheses negative 2 close parentheses squared plus 4 open parentheses negative 2 close parentheses plus 21 end cell row cell f open parentheses negative 2 close parentheses end cell equals cell negative 3 open parentheses 4 close parentheses minus 8 plus 21 end cell row cell f open parentheses negative 2 close parentheses end cell equals cell negative 12 plus 13 end cell row cell f left parenthesis negative 2 right parenthesis end cell equals 1 row blank blank blank row cell g open parentheses x close parentheses end cell equals cell x squared minus 7 x minus 10 end cell row cell g open parentheses 3 close parentheses end cell equals cell open parentheses 3 close parentheses squared minus 7 open parentheses 3 close parentheses minus 10 end cell row cell g open parentheses 3 close parentheses end cell equals cell open parentheses 9 close parentheses minus 21 minus 10 end cell row cell g left parenthesis 3 right parenthesis end cell equals cell negative 22 end cell row blank blank blank row cell open parentheses f minus g close parentheses open parentheses x close parentheses end cell equals cell negative 4 x squared plus 11 x plus 31 end cell row cell open parentheses f minus g close parentheses open parentheses negative 1 close parentheses end cell equals cell negative 4 open parentheses negative 1 close parentheses squared plus 11 open parentheses negative 1 close parentheses plus 31 end cell row cell open parentheses f minus g close parentheses open parentheses negative 1 close parentheses end cell equals cell negative 4 open parentheses 1 close parentheses minus 11 plus 31 end cell row cell left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end cell equals cell negative 4 plus 20 end cell row cell left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end cell equals 16 end table end style

Jadi,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 2 right parenthesis plus g left parenthesis 3 right parenthesis minus left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end cell equals cell 1 plus left parenthesis negative 22 right parenthesis minus 16 end cell row blank equals cell negative 37 end cell end table end style

Dengan demikian, rumus fungsi begin mathsize 14px style left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end style dan nilai begin mathsize 14px style f left parenthesis negative 2 right parenthesis plus g left parenthesis 3 right parenthesis minus left parenthesis f minus g right parenthesis left parenthesis negative 1 right parenthesis end style berturut-turut adalah begin mathsize 14px style negative 4 x squared plus 11 x plus 31 end style dan begin mathsize 14px style negative 37 end style.

Jadi, jawaban yang tepat adalah E.

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