Problem 442 (difficulty: 3/10)

Find an \(\displaystyle f\) and \(\displaystyle g\) such that \(\displaystyle \lim\limits_{x\to \alpha}f(x)=\beta\), \(\displaystyle \lim\limits_{x\to \beta}g(x)=\gamma\), but \(\displaystyle \lim\limits_{x\to \alpha}g(f(x))\neq\gamma\).

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