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This is from Calculus I test, that I failed to solve correctly. This really bugs me, because for Solve[y == Log[E, 3 - 2x] / Sqrt[x + 1], x], the Mathematica is telling me that: "The equations appear to involve the variables to be solved for in an essentially non-algebraic way.".

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I assume that the answer is $x \in \mathbb{R}$

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up vote 2 down vote accepted

Just observe that at $\lim_{x\to -1^+} y(x) = \infty$ and $\lim_{x \to 3/2^-} y(x) = -\infty$ and $y(x)$ is continuous on $x \in (-1, 3/2)$. Therefore the range is indeed $(-\infty,\infty)$.

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