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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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