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Differential Equations

JEE Main 2024 (Online) 9th April Evening Shift

INTEGER+4 / -12024

For a differentiable function \(f: \mathbb{R} \rightarrow \mathbb{R}\), suppose \(f^{\prime}(x)=3 f(x)+\alpha\), where \(\alpha \in \mathbb{R}, f(0)=1\) and \(\lim _\limits{x \rightarrow-\infty} f(x)=7\). Then \(9 f\left(-\log _e 3\right)\) is equal to _________.

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