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Diketahui  dan . Jika  dan  dengan , maka nilai  adalah ....

Pertanyaan

Diketahui f open parentheses x close parentheses equals 2 x squared plus a x plus 2 dan g open parentheses x close parentheses equals a x squared plus 4 x minus 3. Jika p open parentheses x close parentheses equals f open parentheses x close parentheses minus g open parentheses x close parentheses dan 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 dengan p apostrophe open parentheses 0 close parentheses equals negative 3, maka nilai q apostrophe open parentheses 0 close parentheses adalah ....

  1. negative 11 over 9 

  2. negative 2 over 3 

  3. 0 

  4. 1 fourth 

  5. 11 over 9 

Pembahasan Soal:

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 

p open parentheses x close parentheses equals f open parentheses x close parentheses minus g open parentheses x close parentheses p open parentheses x close parentheses equals open parentheses 2 x squared plus a x plus 2 close parentheses minus open parentheses a x squared plus 4 x minus 3 close parentheses p open parentheses x close parentheses equals 2 x squared plus a x plus 2 minus a x squared minus 4 x plus 3 p open parentheses x close parentheses equals 2 x squared minus a x squared plus a x minus 4 x plus 2 plus 3 p open parentheses x close parentheses equals open parentheses 2 minus a close parentheses x squared plus open parentheses a minus 4 close parentheses x plus 5 

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

space p open parentheses x close parentheses equals open parentheses 2 minus a close parentheses x squared plus open parentheses a minus 4 close parentheses x plus 5 p apostrophe open parentheses x close parentheses equals 2 open parentheses 2 minus a close parentheses x plus open parentheses a minus 4 close parentheses p apostrophe open parentheses 0 close parentheses equals 2 open parentheses 2 minus a close parentheses open parentheses 0 close parentheses plus open parentheses a minus 4 close parentheses space space minus 3 equals 0 plus open parentheses a minus 4 close parentheses space space minus 3 equals a minus 4 a minus 4 equals negative 3 space space space space space a equals negative 3 plus 4 space space space space space a equals 1 

- 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.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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