If-f-x-x-2-2x-8-x-2-7x-12-then-find-f-1-x-

Question Number 165687 by mnjuly1970 last updated on 06/Feb/22

I f f (x) = \frac{x^{2} - 2 x - 8}{x^{2} - 7 x + 12}

t h e n, f i n d : f^{- 1} (x) = ?

Answered by TheSupreme last updated on 07/Feb/22

D = R - {4, 3}

f (x) = \frac{(x - 4) (x + 2)}{(x - 4) (x - 3)} = \frac{x + 2}{x - 3} = 1 + \frac{5}{x - 3}

y - 1 = \frac{5}{f^{-} (y) - 3}

f^{- 1} (y) = 3 + \frac{5}{y - 1}

Answered by Rasheed.Sindhi last updated on 06/Feb/22

f (x) = \frac{x^{2} - 2 x - 8}{x^{2} - 7 x + 12} = \frac{(x - 4) (x + 2)}{(x - 4) (x - 3)}

y = \frac{x + 2}{x - 3} = \frac{x - 3 + 5}{x - 3} = 1 + \frac{5}{x - 3}

y - 1 = \frac{5}{x - 3}

x - 3 = \frac{5}{y - 1} \Rightarrow x = \frac{5}{y - 1} + 3 = \frac{3 y - 3 + 5}{y - 1}

x = \frac{3 y + 2}{y - 1}

E x c h a n g i n g x & y

y = \frac{3 x + 2}{x - 1}

∴ f^{- 1} (x) = \frac{3 x + 2}{x - 1}