Let f: (0, ∞) → ℝ be a twice differentiable function. If for some… | JEE Main 2025 Mathematics PYQ

NVAMediumJEE Main 2025 · 29 January, Shift 1Linear Differential Equations

Let $f : (0, \infty) \to \mathbb{R}$ be a twice differentiable function. If for some $a \neq 0$ , $\int_0^1 f(\lambda x) \, d\lambda = a f(x)$ , $f(1) = 1$ and $f(16) = \frac{1}{8}$ , then $16 - f'\left( \frac{1}{16} \right)$ is equal to:

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