which-is-not-range-of-f-x-2x-1-x-2-1-2-2-3-3-10-4-2-3-

Question Number 180827 by sciencestudent last updated on 17/Nov/22

w h i c h i s n o t r a n g e o f f (x) = \frac{2 x + 1}{x - 2} ?

1) 2 2) 3 3) 10 4) \frac{2}{3}

Commented by kaivan.ahmadi last updated on 17/Nov/22

w e k n o w t h a t R_{f} = D_{f^{- 1}}

y = \frac{2 x + 1}{x - 2} \Rightarrow 2 x + 1 = y x - 2 y \Rightarrow (y - 2) x = 1 + 2 y

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

D_{f^{- 1}} = R - {2} = R_{f}

s o 2 \notin R_{f}