Pertanyaan

Diketahui f ( x ) = x − 1 x 2 − 2 x + 6 . Tentukan: b. nilai f ( 2 )

Diketahui $f (x) = \frac{x ^{2} - 2 x + 6}{x - 1}$ . Tentukan:

b. nilai $f (2)$

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style u equals x squared minus 2 x plus 6 space space space space space space space space space space space space space v equals open parentheses x minus 1 close parentheses u apostrophe equals 2 x minus 2 space space space space space space space space space space space space space space space space space space space v apostrophe equals 1 f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction space space space space space space space equals fraction numerator open parentheses 2 x minus 2 close parentheses open parentheses x minus 1 close parentheses minus 1 open parentheses x squared minus 2 x plus 6 close parentheses over denominator open parentheses x minus 1 close parentheses squared end fraction space space space space space space space equals fraction numerator 4 x squared minus 4 x plus 2 minus x squared plus 2 x minus 6 over denominator x squared minus 2 x plus 1 end fraction space space space space space space space equals fraction numerator 3 x squared minus 2 x minus 4 over denominator x squared minus 2 x plus 1 end fraction u equals 3 x squared minus 2 x minus 4 space space space space space space space space space space space space v equals x squared minus 2 x plus 1 u apostrophe equals 6 x minus 2 space space space space space space space space space space space space space space space space space space space space v apostrophe equals 2 x minus 2 f apostrophe apostrophe open parentheses x close parentheses equals fraction numerator open parentheses 6 x minus 2 close parentheses open parentheses x squared minus 2 x plus 1 close parentheses minus open parentheses 2 x minus 2 close parentheses open parentheses 3 x squared minus 2 x minus 4 close parentheses over denominator open parentheses x squared minus 2 x plus 1 close parentheses squared end fraction space space space space space space space space equals fraction numerator negative 16 x squared plus 22 x plus 6 over denominator open parentheses x squared minus 2 x plus 1 close parentheses squared end fraction f double apostrophe open parentheses 2 close parentheses equals fraction numerator negative 16 open parentheses 2 close parentheses squared plus 22 open parentheses 2 close parentheses plus 6 over denominator open parentheses 2 squared minus 2 times 2 plus 1 close parentheses squared end fraction space space space space space space space space space equals fraction numerator negative 14 over denominator 1 end fraction equals negative 14 space end style$