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Range over some other range!

Algebra Level 2

Given $y=\frac{2x}{1+x^{2}}$ , where $x$ and $y$ are real numbers, what is the range of $y^{2}+y-2$ ?

\left[-\frac{9}{4},1\right]

\left[-1,1\right]

\left[0,1\right]

\left[-\frac{9}{4},0 \right]

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by Sandeep Bhardwaj

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