We want to find sufficient and necessary conditions for $f:\mathbb{R}\rightarrow\mathbb{R}$ and $g:\mathbb{R}\rightarrow\mathbb{R}$ to be adjoints with the usual order in $\mathbb{R}$, i.e $$f(x)\leq y\;\Leftrightarrow\; x\leq g(y).$$
Hint: It is necessary that $f,g$ are lower semicontinuous and upper semicontinuous respectively, and of course they have to be nondecreasing functions. In addition, they said we need another sufficient condition.
I have no idea how to start, even I don't understand the hint.
Any hint or idea you can give me, I would be thankful.