TITLE: Questions about total bounded functions
QUESTION [0 upvotes]: Let $f(x)=\sin(x)$ on $x \in[0,2\pi]$.  Find two increasing functions $h$ and $g$ such that $f=g-h$ on $x \in [0, 2\pi]$.
Finding the explicit example is where I'm stuck.  Since this is a bounded function of finite tototal variation I know an explicit $h$ and $g$ exists.  I just don't know what it is.

REPLY [0 votes]: Hint: $g$ can be any function for which $g'$ is large enough.
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