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Diketahui  dan . Rumus fungsi (f+g)(x) dan nilai f(2)−g(−1)+(f+g)(3) adalah ....

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared minus x plus 13 end style dan begin mathsize 14px style g open parentheses x close parentheses equals negative 3 x squared plus 5 x minus 8 end style. Rumus fungsi begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis x right parenthesis end style dan nilai begin mathsize 14px style f left parenthesis 2 right parenthesis minus g left parenthesis negative 1 right parenthesis plus left parenthesis f plus g right parenthesis left parenthesis 3 right parenthesis end style adalah ....

  1. begin mathsize 14px style negative x squared plus 4 x plus 5 end style dan begin mathsize 14px style 11 end style

  2.  undefined dan begin mathsize 14px style 37 end style

  3. undefined dan size 14px 43

  4. undefined dan size 14px 47

  5. size 14px minus size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 5 dan size 14px 61

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Pertama kita cari rumus fungsi untuk begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis x right parenthesis end style. Karena begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end style, maka kita peroleh

 begin mathsize 14px style open parentheses f plus g close parentheses open parentheses x close parentheses equals f open parentheses x close parentheses plus g open parentheses x close parentheses open parentheses f plus g close parentheses open parentheses x close parentheses equals open parentheses 2 x squared minus x plus 13 close parentheses plus open parentheses negative 3 x squared plus 5 x minus 8 close parentheses open parentheses f plus g close parentheses open parentheses x close parentheses equals negative x squared plus 4 x plus 5 end style

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

begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared minus x plus 13 blank f open parentheses 2 close parentheses equals 2 open parentheses 2 close parentheses squared minus 2 plus 13 f open parentheses 2 close parentheses equals 2 open parentheses 4 close parentheses plus 11 f open parentheses 2 close parentheses equals 8 plus 11 equals 19  g open parentheses x close parentheses equals blank minus 3 x squared plus 5 x minus 8 g open parentheses negative 1 close parentheses equals negative 3 open parentheses negative 1 close parentheses squared plus 5 open parentheses negative 1 close parentheses minus 8 g open parentheses negative 1 close parentheses equals negative 3 open parentheses 1 close parentheses minus 5 minus 8 g open parentheses negative 1 close parentheses equals negative 3 minus 13 equals negative 16  open parentheses f plus g close parentheses open parentheses x close parentheses equals negative x squared plus 4 x plus 5 open parentheses f plus g close parentheses open parentheses 3 close parentheses equals negative open parentheses 3 close parentheses squared plus 4 open parentheses 3 close parentheses plus 5 open parentheses f plus g close parentheses open parentheses 3 close parentheses equals negative 9 plus 12 plus 5 equals 8 end style

sehingga kita peroleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 right parenthesis minus g left parenthesis negative 1 right parenthesis plus left parenthesis f plus g right parenthesis left parenthesis 3 right parenthesis end cell equals cell 19 minus left parenthesis negative 16 right parenthesis plus 8 end cell row blank equals 43 end table end style

 

Jadi, jawaban yang tepat adalah C.

42

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