Here is a strange math problem.
Suppose $f:[0,1] \to [0,1]$ is function whose limit exists everywhere.
i.e $g(t) = \lim_{x \to t} f(x)$ is well defined, and gives rise to another function.
Now suppose $f$ and the limit function $g$ satisfy
$$ f(x) = 2g(x) - \sin x \quad \forall x \in [0,1]$$
Find all such $f$.
[Solution]
Suppose $f:[0,1] \to [0,1]$ is function whose limit exists everywhere.
i.e $g(t) = \lim_{x \to t} f(x)$ is well defined, and gives rise to another function.
Now suppose $f$ and the limit function $g$ satisfy
$$ f(x) = 2g(x) - \sin x \quad \forall x \in [0,1]$$
Find all such $f$.
[Solution]
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