Let-f-R-3-5-R-be-defined-by-f-x-3x-2-5x-3-Then-a-f-1-x-x-b-f-1-x-f-x-c-fof-x-x-d-f-1-x-1-19-f-x-

Question Number 13601 by Tinkutara last updated on 21/May/17

Let f : R - {\frac{3}{5}} \to R be defined by

f (x) = \frac{3 x + 2}{5 x - 3} . Then,

(a) f^{- 1} (x) = x

(b) f^{- 1} (x) = - f (x)

(c) f o f (x) = - x

(d) f^{- 1} (x) = \frac{1}{19} f (x)

Answered by mrW1 last updated on 21/May/17

y = \frac{3 x + 2}{5 x - 3}

5 y x - 3 y = 3 x + 2

(5 y - 3) x = 3 y + 2

x = \frac{3 y + 2}{5 y - 3}

\Rightarrow f^{- 1} (x) = \frac{3 x + 2}{5 x - 3} = f (x)

f o f (x) = \frac{3 (\frac{3 x + 2}{5 x - 3}) + 2}{5 (\frac{3 x + 2}{5 x - 3}) - 3} = \frac{9 x + 6 + 10 x - 6}{15 x + 10 - 15 x + 9} = \frac{19 x}{19} = x

n o a n s w e r s e e m s t o b e t r u e \dots

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