Diberikan  dan . Rumus fungsi (f+g)(x) dan nilai dari f(3)−g(7)+(f+g)(−2) secara berturut-turut adalah ....

Pertanyaan

Diberikan begin mathsize 14px style f open parentheses x close parentheses equals 4 x squared plus 5 x minus 30 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 9 x squared minus 2 x plus 25 end style. Rumus fungsi undefined dan nilai dari begin mathsize 14px style f left parenthesis 3 right parenthesis minus g left parenthesis 7 right parenthesis plus left parenthesis f plus g right parenthesis left parenthesis negative 2 right parenthesis end style secara berturut-turut adalah ....

  1. begin mathsize 14px style 13 x squared plus 3 x plus 5 end style dan begin mathsize 14px style negative 400 end style 

  2. undefined dan begin mathsize 14px style negative 380 end style 

  3. size 14px 13 size 14px x to the power of size 14px 2 size 14px plus size 14px 3 size 14px x size 14px minus size 14px 5 danblank size 14px 514 

  4. undefined dan size 14px minus size 14px 390 

  5. undefined dan size 14px minus size 14px 12  

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawabannya adalah D.

Pembahasan

Pertama, akan dicari rumus fungsi untuk undefined.

Perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell begin mathsize 14px style left parenthesis f plus g right parenthesis end style begin mathsize 14px style left parenthesis x right parenthesis end style end cell size 14px equals cell size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px g begin mathsize 14px style left parenthesis x right parenthesis end style end cell row blank size 14px equals cell size 14px 4 size 14px x to the power of size 14px 2 size 14px plus size 14px 5 size 14px x size 14px minus size 14px 30 size 14px plus size 14px 9 size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px plus size 14px 25 end cell row blank size 14px equals cell size 14px 13 size 14px x to the power of size 14px 2 size 14px plus size 14px 3 size 14px x size 14px minus size 14px 5 end cell end table  

Selanjutnya akan dicari masing-masing nilai dari  begin mathsize 14px style f left parenthesis 3 right parenthesis comma space g left parenthesis 7 right parenthesis comma end style dan begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis negative 2 right parenthesis end style.

Substitusikan begin mathsize 14px style x equals 3 end style ke dalam begin mathsize 14px style f left parenthesis x right parenthesis end style, didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f begin mathsize 14px style left parenthesis 3 right parenthesis end style end cell size 14px equals cell size 14px 4 begin mathsize 14px style left parenthesis 3 right parenthesis end style to the power of size 14px 2 size 14px plus size 14px 5 begin mathsize 14px style left parenthesis 3 right parenthesis end style size 14px minus size 14px 30 end cell row blank size 14px equals cell size 14px 4 begin mathsize 14px style left parenthesis 9 right parenthesis end style size 14px plus size 14px 15 size 14px minus size 14px 30 end cell row blank size 14px equals cell size 14px 36 size 14px minus size 14px 15 end cell row blank size 14px equals size 14px 21 end table

Maka begin mathsize 14px style f left parenthesis 3 right parenthesis equals 21 end style.

Kemudian, Substitusikan begin mathsize 14px style x equals 7 end style ke dalam begin mathsize 14px style g left parenthesis x right parenthesis end style, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px g begin mathsize 14px style left parenthesis 7 right parenthesis end style end cell size 14px equals cell size 14px 9 begin mathsize 14px style left parenthesis 7 right parenthesis end style to the power of size 14px 2 size 14px minus size 14px 2 begin mathsize 14px style left parenthesis 7 right parenthesis end style size 14px plus size 14px 25 end cell row blank size 14px equals cell size 14px 9 begin mathsize 14px style left parenthesis 49 right parenthesis end style size 14px minus size 14px 14 size 14px plus size 14px 25 end cell row blank size 14px equals cell size 14px 441 size 14px plus size 14px 11 end cell row blank size 14px equals size 14px 452 end table

Maka begin mathsize 14px style g left parenthesis 7 right parenthesis equals 452 end style.

Selanjutnya, substitusikan begin mathsize 14px style x equals negative 2 end style ke dalam undefined, didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell begin mathsize 14px style left parenthesis f plus g right parenthesis end style begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell size 14px 13 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style to the power of size 14px 2 size 14px plus size 14px 3 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px minus size 14px 5 end cell row blank size 14px equals cell size 14px 13 begin mathsize 14px style left parenthesis 4 right parenthesis end style size 14px minus size 14px 6 size 14px minus size 14px 5 size 14px equals size 14px 52 size 14px minus size 14px 11 end cell row blank size 14px equals size 14px 41 end table

Maka begin mathsize 14px style left parenthesis f plus g right parenthesis left parenthesis negative 2 right parenthesis equals 41 end style

Sehingga diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 3 right parenthesis minus g left parenthesis 7 right parenthesis plus left parenthesis f plus g right parenthesis left parenthesis negative 2 right parenthesis end cell equals cell 21 minus 452 plus 41 end cell row blank equals cell negative 390 end cell end table end style

Jadi, jawabannya adalah D.

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