Jika f(x+2) = 2x - 5 / 3x + 10, maka nilai x yang memenuhi ([tex] f^{-1} o f^{-1} [/tex]) (2x +1) = 1 adalah...
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Jika f(x+2) = 2x - 5 / 3x + 10, maka nilai x yang memenuhi ([tex] f^{-1} o f^{-1} [/tex]) (2x +1) = 1 adalah...
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1. Jawaban whongaliem
f (x + 2) = (2x - 5) / (3x + 10)
f (x) = {2(x - 2) - 5} / {3 (x - 2) + 10}
= (2x - 4 - 5) / (3x - 6 + 10)
= (2x - 9) / (3x + 4)
f^-1 (x) = (- 4x - 9) / (3x - 2)
[tex] f^{- 1} o f^{- 1} (x) = \frac{- 4( \frac{- 4x - 9}{3x - 2}) - 9 }{3( \frac{-4x - 9}{3x - 2}) - 2 } .... kalikan dgn (3x - 2)[/tex]
[tex]= \frac{- 4 (- 4x - 9) - 9 (3x - 2)}{3 ( - 4x - 9) - 2(3x - 2)} [/tex]
[tex]= \frac{16x + 36 - 27x + 18}{- 12x - 27 - 6x + 4} [/tex]
[tex]= \frac{- 11x + 54}{- 18x - 23} [/tex]
[tex] f^{-1} o f^{-1}(2x - 1) = \frac{- 11(2x - 1) + 54}{- 18 (2x - 1) - 23} [/tex]
[tex]1 = \frac{- 22x + 11 + 54}{- 36x + 18 - 23} [/tex]
[tex]1 = \frac{ - 22x + 65}{- 36x - 5} [/tex]
- 36x - 5 = - 22x + 65
- 36x + 22x = 65 + 5
- 14x = 70
x = 70 / - 14
x = 5