Pertanyaan

Diketahui f ( x ) = 2 x 2 + a x + 2 dan g ( x ) = a x 2 + 4 x − 3 . Jika p ( x ) = f ( x ) − g ( x ) dan q ( x ) = g ( x ) f ( x ) dengan p ( 0 ) = − 3 , maka nilai q ( 0 ) adalah ....

Diketahui $f (x) = 2 x^{2} + a x + 2$ dan $g (x) = a x^{2} + 4 x - 3$ . Jika $p (x) = f (x) - g (x)$ dan $q (x) = \frac{f ( x )}{g ( x )}$ dengan $p (0) = - 3$ , maka nilai $q (0)$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Diketahui: Maka: - Menentukan fungsi - Diketahui , nilai : - Menentukan fungsi - Menentukan fungsi - Menentukan fungsi Misalkan: Sehingga: Jadi, jawaban yang benar adalah A.

Diketahui:

$f open parentheses x close parentheses equals 2 x squared plus a x plus 2 g open parentheses x close parentheses equals a x squared plus 4 x minus 3 p open parentheses x close parentheses equals f open parentheses x close parentheses minus g open parentheses x close parentheses q open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction p apostrophe open parentheses 0 close parentheses equals negative 3$

Maka:

- Menentukan fungsi p open parentheses x close parentheses

- Diketahui p apostrophe open parentheses 0 close parentheses equals negative 3 , nilai :

- Menentukan fungsi f open parentheses x close parentheses

f open parentheses x close parentheses equals 2 x squared plus a x plus 2 f open parentheses x close parentheses equals 2 x squared plus open parentheses 1 close parentheses x plus 2 f open parentheses x close parentheses equals 2 x squared plus x plus 2

- Menentukan fungsi g open parentheses x close parentheses

g open parentheses x close parentheses equals a x squared plus 4 x minus 3 g open parentheses x close parentheses equals open parentheses 1 close parentheses x squared plus 4 x minus 3 g open parentheses x close parentheses equals x squared plus 4 x minus 3

- Menentukan fungsi q open parentheses x close parentheses

$q open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction q open parentheses x close parentheses equals fraction numerator 2 x squared plus x plus 2 over denominator x squared plus 4 x minus 3 end fraction$

Misalkan:

u equals 2 x squared plus x plus 2 space rightwards arrow space u apostrophe equals 4 x plus 1 v equals x squared plus 4 x minus 3 space rightwards arrow space v apostrophe equals 2 x plus 4

Sehingga:

$space q open parentheses x close parentheses equals u over v q apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction q apostrophe open parentheses x close parentheses equals fraction numerator open parentheses 4 x plus 1 close parentheses times open parentheses x squared plus 4 x minus 3 close parentheses minus open parentheses 2 x squared plus x plus 2 close parentheses times open parentheses 2 x plus 4 close parentheses over denominator open parentheses x squared plus 4 x minus 3 close parentheses squared end fraction q apostrophe open parentheses 0 close parentheses equals fraction numerator open parentheses 4 times 0 plus 1 close parentheses times open parentheses 0 squared plus 4 times 0 minus 3 close parentheses minus open parentheses 2 times 0 squared plus 0 plus 2 close parentheses times open parentheses 2 times 0 plus 4 close parentheses over denominator open parentheses 0 squared plus 4 times 0 minus 3 close parentheses squared end fraction q apostrophe open parentheses 0 close parentheses equals fraction numerator open parentheses 0 plus 1 close parentheses times open parentheses 0 plus 0 minus 3 close parentheses minus open parentheses 0 plus 0 plus 2 close parentheses times open parentheses 0 plus 4 close parentheses over denominator open parentheses 0 plus 0 minus 3 close parentheses squared end fraction q apostrophe open parentheses 0 close parentheses equals fraction numerator open parentheses 1 close parentheses times open parentheses negative 3 close parentheses minus open parentheses 2 close parentheses times open parentheses 4 close parentheses over denominator open parentheses negative 3 close parentheses squared end fraction q apostrophe open parentheses 0 close parentheses equals fraction numerator negative 3 minus 8 over denominator 9 end fraction q apostrophe open parentheses 0 close parentheses equals fraction numerator negative 11 over denominator 9 end fraction$

Jadi, jawaban yang benar adalah A.