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Let $r$ be a real number and $f(x)=\left\{\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { if } x<r\end{array}\right.$. Then, the equation $f(x)=f(f(x))$ holds for all real values of $x$ where

1. $x \leq r$
2. $x>r$
3. $x \geq r$
4. $x \neq r$

Ans is A.

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