Question 171
Consider a strictly monotone function $f: \mathbb{R} \rightarrow \mathbb{R}$. Determine all functions $g: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
f(g(x+2017)) \geq f(x) \geq f(g(x)+2017),\; \forall x \in \mathbb{R}
$$
$$
f(g(x+2017)) \geq f(x) \geq f(g(x)+2017),\; \forall x \in \mathbb{R}
$$