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Mathematics · 2024

JEE Main · 9 April 2024, Shift 2 · Q26

For a differentiable function f: R → R, suppose f^′(x)=3 f(x)+α, where α ∈ R, f(0)=1 and lim_x →-∞ f(x)=7. Then 9 f(- log_e 3) is equal to ____.

For a differentiable function $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$, suppose $\displaystyle f^{\prime}(x)=3 f(x)+\alpha$, where $\displaystyle \alpha \in \mathbb{R}$, $\displaystyle f(0)=1$ and $\displaystyle \lim _{x \rightarrow-\infty} f(x)=7$. Then $\displaystyle 9 f\left(-\log _e 3\right)$ is equal to $\displaystyle \_\_\_\_$.
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JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.