If-f-x-x-3-x-1-and-h-x-f-f-f-f-2022-times-f-x-then-h-1-

Question Number 142674 by Snail last updated on 03/Jun/21

I f f (x) = \frac{x - 3}{x + 1} a n d h (x) = f (f (f (f (. . 2022 t i m e s (f (x))))))

t h e n h (1) = ?

Answered by iloveisrael last updated on 04/Jun/21

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

f (f (x)) = \frac{- 2 x - 6}{2 x - 2} = \frac{- x - 3}{x - 1} = f^{- 1} (x)

Extra \left or missing \right

h (x) = x \Rightarrow h (1) = 1