Let \( f \) be any function defined on \( R \) and let it satisfy the condition: \[ |f(x)-f(y)| ...

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Let \( f \) be any function defined on \( R \) and let it satisfy the condition:
\[
|f(x)-f(y)| \leq\left|(x-y)^{2}\right|, \forall(x, y) \in R
\]
If \( f(0)=1 \), then
(a) \( f(x) \) can take any value in \( R \)
(b) \( f(x)0, \forall x \in R \)
(c) \( f(x)=0, \forall x \in R \)
(d) \( f(x)0, \forall x \in R \)
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