Find the domain and range of the function, f(x)=((x^2 +2)/(2x+1)) Mastermind


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Question Number 171032 by Mastermind last updated on 06/Jun/22

$F i n d t h e d o m a i n a n d r a n g e o f t h e$ $f u n c t i o n, f (x) = \frac{x^{2} + 2}{2 x + 1}$ $M a s t e r m i n d$
	Answered by cortano1 last updated on 06/Jun/22

	$D_{f} = x \neq - \frac{1}{2}; x \in R$ $2 x y + y = x^{2} + 2$ $\Rightarrow x^{2} - 2 x y + 2 - y = 0$ $\Rightarrow Δ = 4 y^{2} - 4.1 . (2 - y) ⩾ 0$ $\Rightarrow y^{2} + y - 2 ⩾ 0$ $\Rightarrow (y + 2) (y - 1) ⩾ 0$ $\Rightarrow R_{f} : y ⩽ - 2 \lor y ⩾ 1$
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