If a function satisfies the relation \( f(x) f^{\prime \prime}(x)-f...

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If a function satisfies the relation \( f(x) f^{\prime \prime}(x)-f(x) f^{\prime}(x)=\left(f^{\prime}(x)\right)^{2} \)
\( \mathrm{P} \) \( \forall x \in R \) and \( f(0)=f^{\prime}(0)=1 \), then

W
Number of roots of the equation \( f(x)=e^{x} \) is
(1) 0
(2) 1
(3) 2
(4) infinite
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