Find-the-domain-and-range-of-the-function-f-x-x-2-2-2x-1-Mastermind-

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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