Let f: ℝ - {0} → ℝ be a function satisfying f(x/y) = f(x)/f(y) fo… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 30 January, Shift 2Linear Differential Equations

Let $f : \mathbb{R} - \{0\} \to \mathbb{R}$ be a function satisfying $f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)}$ for all $x, y$ with $f(y) \neq 0$ . If $f'(1) = 2024$ , then:

A
$xf'(x) - 2024f(x) = 0$
B
$xf(x) + 2024f(x) = 0$
C
$f(x) + xf'(x) = 2024$
D
$xf(x) - 2023f(x) = 0$

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