# Calculus in functional equation

Calculus Level pending

Let $$f: \mathbb R \to \mathbb R$$ satisfy $$| f(x+y) - f(x-y) - y | \leq y^2$$ for all $$(x,y) \in \mathbb R^2$$.

Determine which of the following can be a possible function of $$f(x)$$.


Note: In the options, $$c$$ denote an arbitrary constant.

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