which is not range of f(x)=((2x+1)/(x−2))? 1) 2 2) 3 3)10 4) (2/3)


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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
$we know that R_f =D_f^(−1) y=((2x+1)/(x−2))⇒2x+1=yx−2y⇒(y−2)x=1+2y ⇒x=((1+2y)/(y−2))⇒f^(−1) (x)=((1+2x)/(x−2)) D_f^(−1) =R−{2}=R_f so 2∉R_f$
$w e k n o w t h a t R_{f} = D_{f^{- 1}}$ $y = \frac{2 x + 1}{x - 2} \Rightarrow 2 x + 1 = y x - 2 y \Rightarrow (y - 2) x = 1 + 2 y$ $\Rightarrow x = \frac{1 + 2 y}{y - 2} \Rightarrow f^{- 1} (x) = \frac{1 + 2 x}{x - 2}$ $D_{f^{- 1}} = R - {2} = R_{f}$ $s o 2 \notin R_{f}$
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