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Pertanyaan

Diberikan fungsi undefined dan undefined dengan begin mathsize 14px style f left parenthesis x right parenthesis equals negative 9 x plus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator 3 x end fraction end style.  Rumus fungsi dari begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis x right parenthesis end style dan nilai dari begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis minus open parentheses f plus 1 over g close parentheses left parenthesis negative 5 right parenthesis end style secara berutrut-turut adalah …. 

  1. begin mathsize 14px style fraction numerator 3 x left parenthesis 1 minus square root of 27 minus 9 x end root right parenthesis over denominator square root of 3 minus x end root end fraction plus 2 end style dan begin mathsize 14px style fraction numerator negative 150 plus 15 square root of 2 over denominator 4 end fraction end style

  2. fraction numerator size 14px 3 size 14px x begin mathsize 14px style left parenthesis 1 plus square root of 27 minus 9 x end root right parenthesis end style over denominator square root of size 14px 3 size 14px minus size 14px x end root end fraction size 14px plus size 14px 2 dan begin mathsize 14px style fraction numerator negative 150 plus 15 square root of 2 over denominator 4 end fraction end style

  3. negative fraction numerator size 14px 3 size 14px x begin mathsize 14px style left parenthesis 1 plus square root of 27 minus 9 x end root right parenthesis end style over denominator square root of size 14px 3 size 14px minus size 14px x end root end fraction size 14px plus size 14px 2 dan fraction numerator size 14px minus size 14px 120 size 14px plus size 14px 15 square root of size 14px 2 over denominator size 14px 4 end fraction

  4. negative fraction numerator size 14px 3 size 14px x begin mathsize 14px style left parenthesis 1 plus square root of 27 minus 9 x end root right parenthesis end style over denominator square root of size 14px 3 size 14px minus size 14px x end root end fraction size 14px plus size 14px 2 dan begin mathsize 14px style fraction numerator negative 158 plus 15 square root of 2 over denominator 4 end fraction end style

  5. fraction numerator size 14px x begin mathsize 14px style open parentheses negative 1 plus square root of 27 minus 9 x end root close parentheses end style over denominator square root of size 14px 3 size 14px minus size 14px x end root end fraction size 14px plus size 14px 2 dan fraction numerator size 14px minus size 14px 128 size 14px plus size 14px 15 square root of size 14px 2 over denominator size 14px 4 end fraction

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A. 

Pembahasan

Dari soal, diberikan fungsi undefined dan undefined dengan begin mathsize 14px style f left parenthesis x right parenthesis equals negative 9 x plus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator 3 x end fraction end style

Akan dicari umus fungsi dari begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis x right parenthesis end style dan nilai dari begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis minus open parentheses f plus 1 over g close parentheses left parenthesis negative 5 right parenthesis end style.

Perhatikan bahwa

undefined

Terdapat bentuk akar sebagai penyebut pada fungsi tersebut. Maka didapat syarat bentuk dalam akar harus positif. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 minus x end cell greater than cell 0 space end cell row cell negative x end cell greater than cell negative 3 end cell row x less than 3 end table end style 

Karena begin mathsize 14px style x equals negative 1 end style dan begin mathsize 14px style x equals negative 5 end style memenuhi begin mathsize 14px style x less than 3 end style, maka begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis end style dan open parentheses size 14px f size 14px plus size 14px 1 over size 14px g close parentheses size 14px left parenthesis size 14px minus size 14px 5 size 14px right parenthesis terdefinisi.

Pertama, akan dicari begin mathsize 14px style open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis end style. Perhatikan bahwa, sebelumnya, diperoleh

undefined

Substitusikan undefined, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis end cell equals cell fraction numerator 3 times left parenthesis negative 1 right parenthesis left parenthesis 1 minus square root of 27 minus 9 times left parenthesis negative 1 right parenthesis end root right parenthesis over denominator begin display style square root of 3 minus left parenthesis negative 1 right parenthesis end root end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 3 left parenthesis 1 minus square root of 27 plus 9 end root right parenthesis over denominator begin display style square root of 3 plus 1 end root end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 3 left parenthesis 1 minus square root of 36 right parenthesis over denominator begin display style square root of 4 end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 3 times left parenthesis negative 5 right parenthesis over denominator begin display style 2 end style end fraction plus 2 end cell row blank equals cell fraction numerator 15 plus 4 over denominator 2 end fraction end cell row blank equals cell 19 over 2 end cell end table end style

Kemudian, substitusikan size 14px x size 14px equals size 14px minus size 14px 5, didapat hasil sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus 1 over g close parentheses left parenthesis negative 5 right parenthesis end cell equals cell fraction numerator 3 times left parenthesis negative 5 right parenthesis left parenthesis 1 minus square root of 27 minus 9 times left parenthesis negative 5 right parenthesis end root right parenthesis over denominator begin display style square root of 3 minus left parenthesis negative 5 right parenthesis end root end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 left parenthesis 1 minus square root of 27 plus 45 end root right parenthesis over denominator begin display style square root of 3 plus 5 end root end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 left parenthesis 1 minus square root of 72 right parenthesis over denominator begin display style square root of 8 end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 left parenthesis 1 minus 6 square root of 2 right parenthesis over denominator begin display style 2 square root of 2 end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 square root of 2 plus 90 square root of 4 over denominator begin display style 4 end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 square root of 2 plus 180 over denominator begin display style 4 end style end fraction plus 2 end cell row blank equals cell fraction numerator negative 15 square root of 2 plus 180 plus 8 over denominator begin display style 4 end style end fraction end cell row blank equals cell fraction numerator negative 15 square root of 2 plus 188 over denominator begin display style 4 end style end fraction end cell end table end style

Sehingga diperoleh hasil sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus 1 over g close parentheses left parenthesis negative 1 right parenthesis minus open parentheses f plus 1 over g close parentheses left parenthesis negative 5 right parenthesis end cell equals cell 19 over 2 minus fraction numerator negative 15 square root of 2 plus 188 over denominator 4 end fraction end cell row blank equals cell fraction numerator 38 minus open parentheses negative 15 square root of 2 plus 188 close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 150 plus 15 square root of 2 over denominator 4 end fraction end cell end table end style

Jadi, jawaban yang tepat adalah A. 

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