Let $f:\mathbb{R}\mapsto\mathbb{R}$ be a one-to-one function with $f(\mathbb{R})=\mathbb{R}$. If $f^{-1}(x)$ is continuous $\forall x\in\mathbb{R}$, prove or disprove that $f(x)$ is continuous $\forall x\in\mathbb{R}$.
2026-04-07 00:21:32.1775521292
If $f^{-1}(x)$ is continuous, is $f(x)$ also continuous?
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