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Pertanyaan

Diberikan size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px minus fraction numerator size 14px 2 size 14px k over denominator size 14px k size 14px x size 14px minus size 14px 1 end fraction dan size 14px g begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals square root of size 14px 2 size 14px x size 14px plus size 14px 6 end root. Jika begin mathsize 14px style left parenthesis 5 g squared times f right parenthesis end style begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px equals size 14px 15, maka nilai dari begin mathsize 14px style 2 k minus 5 end style adalah ....

  1. begin mathsize 14px style negative 11 end style

  2. begin mathsize 14px style negative 8 end style

  3. size 14px minus size 14px 19 over size 14px 3

  4. size 14px minus size 14px 11 over size 14px 3 

  5. begin mathsize 14px style 8 end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawabannya adalah B.

Pembahasan

Ingat kembali bahwa begin mathsize 14px style left parenthesis g times f right parenthesis left parenthesis x right parenthesis equals g left parenthesis x right parenthesis times f left parenthesis x right parenthesis end style. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 5 g squared times f right parenthesis left parenthesis x right parenthesis end cell equals cell left parenthesis 5 g times g times f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell 5 times g left parenthesis x right parenthesis times g left parenthesis x right parenthesis times f left parenthesis x right parenthesis end cell end table end style

Substitusikan size 14px x size 14px equals size 14px minus size 14px 2, maka

size 14px left parenthesis size 14px 5 size 14px g to the power of size 14px 2 size 14px times size 14px f size 14px right parenthesis begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px equals size 14px 5 size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style.

Akan dicari nilai dari  begin mathsize 14px style f left parenthesis negative 2 right parenthesis end style dan  begin mathsize 14px style g left parenthesis negative 2 right parenthesis end style terlebih dahulu.

Perhatikan bahwa nilai dari begin mathsize 14px style f left parenthesis negative 2 right parenthesis end style adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell size 14px minus fraction numerator size 14px 2 size 14px k over denominator size 14px k begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px minus size 14px 1 end fraction end cell row blank size 14px equals cell size 14px minus fraction numerator size 14px 2 size 14px k over denominator size 14px minus size 14px 2 size 14px k size 14px minus size 14px 1 end fraction end cell row blank size 14px equals cell fraction numerator size 14px 2 size 14px k over denominator size 14px 2 size 14px k size 14px plus size 14px 1 end fraction end cell end table

dan nilai dari undefined adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell square root of size 14px 2 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px plus size 14px 6 end root end cell row blank size 14px equals cell square root of size 14px minus size 14px 4 size 14px plus size 14px 6 end root end cell row blank size 14px equals cell square root of size 14px 2 end cell end table 

Maka, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px left parenthesis size 14px 5 size 14px g to the power of size 14px 2 size 14px times size 14px f size 14px right parenthesis begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell size 14px equals cell size 14px 5 size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px g begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px times size 14px f begin mathsize 14px style left parenthesis negative 2 right parenthesis end style end cell row size 14px 15 size 14px equals cell size 14px 5 begin mathsize 14px style left parenthesis square root of 2 right parenthesis end style begin mathsize 14px style left parenthesis square root of 2 right parenthesis end style begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row size 14px 15 size 14px equals cell size 14px 5 size 14px times size 14px 2 begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row size 14px 3 size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis fraction numerator 2 k over denominator 2 k plus 1 end fraction right parenthesis end style end cell row cell size 14px 3 begin mathsize 14px style left parenthesis 2 k plus 1 right parenthesis end style end cell size 14px equals cell size 14px 2 size 14px times size 14px 2 size 14px k end cell row cell size 14px 6 size 14px k size 14px plus size 14px 3 end cell size 14px equals cell size 14px 4 size 14px k end cell row cell size 14px 6 size 14px k size 14px minus size 14px 4 size 14px k end cell size 14px equals cell size 14px minus size 14px 3 end cell row cell size 14px 2 size 14px k end cell size 14px equals cell size 14px minus size 14px 3 end cell row size 14px k size 14px equals cell size 14px minus size 14px 3 over size 14px 2 end cell end table 

Sehingga didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px 2 size 14px k size 14px minus size 14px 5 end cell size 14px equals cell size 14px 2 begin mathsize 14px style left parenthesis negative 3 over 2 right parenthesis end style size 14px minus size 14px 5 end cell row blank size 14px equals cell size 14px minus size 14px 3 size 14px minus size 14px 5 end cell row blank size 14px equals cell size 14px minus size 14px 8 end cell end table 

Jadi, jawabannya adalah B.

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