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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