Uncreative Function

This is a user suggested problem. The TopsOJ staff thanks and gives full credit to yujhtheyujh for their contribution.

Let f(x) + 45f(\dfrac{1}{x}) = 2024\cdot x for all x \in \mathbb{R} in its domain. Find the the absolute value of the sum of all k such that k \in \mathbb{Z} and f(k) \in \mathbb{Z}^+.