Let \( \mathrm{f}:[0,1] \rightarrow R \) be such that \( \mathrm{f}...

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Let \( \mathrm{f}:[0,1] \rightarrow R \) be such that \( \mathrm{f}(\mathrm{xy})=\mathrm{f}(\mathrm{x}) \mathrm{f}(\mathrm{y}) \) for all \( \mathrm{x}, \mathrm{y} \in[0 \), \( 1] \), and \( f(0) \neq 0 \). If \( y=y(x) \) satisfies the differential equation,
P \( \frac{d y}{d x}=f(x) \) with \( y(0)=1 \), then \( y\left(\frac{1}{4}\right)+y\left(\frac{3}{4}\right) \) is equal to :-

W)
[JEE Main - 2019 (January)]
(a) 4
(b) 3
(c) 5
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