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Diberikan fungsi f:R→R dengan f(x)=x2−3​9x2+12x−18​−5−x3x​. Nilai dari f(2)+f(7​) adalah ….

Pertanyaan

Diberikan fungsi begin mathsize 14px style f colon straight real numbers rightwards arrow straight real numbers end style dengan begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 9 x squared plus 12 x minus 18 over denominator square root of x squared minus 3 end root end fraction minus fraction numerator 3 x over denominator 5 minus x end fraction end style. Nilai dari begin mathsize 14px style f left parenthesis 2 right parenthesis plus f left parenthesis square root of 7 right parenthesis end style adalah ….

  1. fraction numerator size 14px 1 size 14px. size 14px 100 size 14px minus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction

  2. fraction numerator size 14px 1 size 14px. size 14px 104 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction

  3. fraction numerator size 14px 1 size 14px. size 14px 104 size 14px minus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction

  4. fraction numerator size 14px 1 size 14px. size 14px 125 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction

  5. fraction numerator size 14px 1 size 14px. size 14px 253 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah B.space space 

Pembahasan

Dari soal, diberikan fungsi begin mathsize 14px style f colon straight real numbers rightwards arrow straight real numbers end style dengan begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 9 x squared plus 12 x minus 18 over denominator square root of x squared minus 3 end root end fraction minus fraction numerator 3 x over denominator 5 minus x end fraction end style. Akan dicari nilai dari begin mathsize 14px style f left parenthesis 2 right parenthesis plus f left parenthesis square root of 7 right parenthesis end style.

Pertama, akan dicari nilai dari begin mathsize 14px style f left parenthesis 2 right parenthesis end style. Substitusikan begin mathsize 14px style x equals 2 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 right parenthesis end cell equals cell fraction numerator 9 times 2 squared plus 12 times 2 minus 18 over denominator square root of 2 squared minus 3 end root end fraction minus fraction numerator 3 times 2 over denominator 5 minus 2 end fraction end cell row blank equals cell fraction numerator 36 plus 24 minus 18 over denominator square root of 4 minus 3 end root end fraction minus 6 over 3 end cell row blank equals cell 42 minus 2 end cell row blank equals 40 end table end style

Kemudian, akan dicari nilai dari begin mathsize 14px style f left parenthesis square root of 7 right parenthesis end style. Substitusikan begin mathsize 14px style x equals square root of 7 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis square root of 7 right parenthesis end cell equals cell fraction numerator 9 times left parenthesis square root of 7 right parenthesis squared plus 12 times square root of 7 minus 18 over denominator square root of open parentheses square root of 7 close parentheses squared minus 3 end root end fraction minus fraction numerator 3 times square root of 7 over denominator 5 minus square root of 7 end fraction end cell row blank equals cell fraction numerator 9 times 7 plus 12 square root of 7 minus 18 over denominator square root of 7 minus 3 end root end fraction minus fraction numerator 3 square root of 7 over denominator 5 minus square root of 7 end fraction end cell row blank equals cell fraction numerator 63 plus 12 square root of 7 minus 18 over denominator square root of 4 end fraction minus fraction numerator 3 square root of 7 over denominator 5 minus square root of 7 end fraction end cell row blank equals cell fraction numerator 45 plus 12 square root of 7 over denominator 2 end fraction minus fraction numerator 3 square root of 7 over denominator 5 minus square root of 7 end fraction end cell end table end style

Dengan merasionalkan pecahan, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 45 plus 12 square root of 7 over denominator 2 end fraction minus fraction numerator 3 square root of 7 over denominator 5 minus square root of 7 end fraction times open parentheses fraction numerator 5 plus square root of 7 over denominator 5 plus square root of 7 end fraction close parentheses end cell row blank equals cell fraction numerator 45 plus 12 square root of 7 over denominator 2 end fraction minus fraction numerator 3 square root of 7 times open parentheses 5 plus square root of 7 close parentheses over denominator 25 minus 7 end fraction end cell row blank equals cell fraction numerator 45 plus 12 square root of 7 over denominator 2 end fraction minus fraction numerator 15 square root of 7 plus 3 times 7 over denominator 18 end fraction end cell row blank equals cell fraction numerator 45 plus 12 square root of 7 over denominator 2 end fraction minus fraction numerator 15 square root of 7 plus 21 over denominator 18 end fraction end cell row blank equals cell fraction numerator 9 open parentheses 45 plus 12 square root of 7 close parentheses minus open parentheses 15 square root of 7 plus 21 close parentheses over denominator 18 end fraction end cell row blank equals cell fraction numerator 405 plus 108 square root of 7 minus 15 square root of 7 minus 21 over denominator 18 end fraction end cell row blank equals cell fraction numerator 384 plus 93 square root of 7 over denominator 18 end fraction end cell end table end style 

Sehingga didapat hasil sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 right parenthesis plus f open parentheses square root of 7 close parentheses end cell equals cell 40 plus fraction numerator 384 plus 93 square root of 7 over denominator 18 end fraction end cell row blank equals cell fraction numerator 720 plus 384 plus 93 square root of 7 over denominator 18 end fraction end cell row blank equals cell fraction numerator 1.104 plus 93 square root of 7 over denominator 18 end fraction end cell end table end style 

Jadi, jawabannya adalah B.space space 

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