QJEEM24Maf5cb: JEE Main 2024 Mathematics - Class 12 JEEM24Maf5cb Solution: For a differentiable function f : R → R , suppose f ′ ( x ) = 3 …

Question

Verified Solution • 2025–26 Session moderate

QJEEM24Maf5cb: JEE Main 2024 Mathematics - Class 12 JEEM24Maf5cb Solution: For a differentiable function f : R → R , suppose f ′ ( x ) = 3 …

For a differentiable function $f : R \to R$ , suppose $f^{'} (x) = 3 f (x) + α$ , where $α \in R, f (0) = 1$ and $lim_{x \to - \infty} f (x) = 7$ . Then $9 f (- \log_{e} 3)$ is equal to _________.

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank

Browse year-wise authentic previous years' questions with solutions

Authentic CBT Mock Tests

Simulate official exam environment with live timer and percentile scoring

Accepted Answer

$\begin{aligned} f^{'} (x) = 3 f (x) + α \\ \Rightarrow \frac{d y}{3 y + α} = d x \\ \Rightarrow \frac{1}{3} \ln (3 y + α) = x + C \\ y (0) = 1 \Rightarrow C = \frac{1}{3} \ln (3 + α) \\ \frac{1}{3} \ln (\frac{3 y + α}{3 + α}) = x \\ \Rightarrow y = \frac{1}{3} ((3 + α) e^{3 x} - α) = f (x) \\ lim_{x \to - \infty} f (x) = 7 \Rightarrow α = - 21 \\ \Rightarrow f (x) = 7 - 6 e^{3 x} \\ 9 f (- \ln 3) = 61 \end{aligned}$

QJEEM24Maf5cb: JEE Main 2024 Mathematics - Class 12 JEEM24Maf5cb Solution: For a differentiable function f : R → R , suppose f ′ ( x ) = 3 …

Step-by-Step Verified Solution

Related Learning Resources & Exam Preparation