Pertanyaan

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

Diberikan fungsi $f : R \to R$ dengan $f (x) = \frac{9 x ^{2} + 12 x - 18}{x ^{2} - 3} - \frac{3 x}{5 - x}$ . Nilai dari $f (2) + f (7)$ adalah ….

$fraction numerator size 14px 1 size 14px. size 14px 100 size 14px minus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction$
$fraction numerator size 14px 1 size 14px. size 14px 104 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction$
$fraction numerator size 14px 1 size 14px. size 14px 104 size 14px minus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction$
$fraction numerator size 14px 1 size 14px. size 14px 125 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction$
$fraction numerator size 14px 1 size 14px. size 14px 253 size 14px plus size 14px 93 square root of size 14px 7 over denominator size 14px 18 end fraction$

N. Putri

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah B.

Pembahasan

Dari soal, diberikanfungsi dengan . Akan dicari nilai dari . Pertama, akan dicari nilai dari . Substitusikan , didapat Kemudian, akan dicari nilai dari . Substitusikan , didapat Dengan merasionalkan pecahan, didapat Sehingga didapat hasil sebagai berikut. Jadi, jawabannya adalah B.

Dari soal, diberikan fungsi 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 .

Pertama, akan dicari nilai dari . Substitusikan , 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 . Substitusikan , 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.