A function \(f : \mathbb{R} \rightarrow \mathbb{R} \) is differentiated \( 2015 \) times to get \( g(x) = \dfrac{ d^{2015} }{dx^{2015} } \big[ f(x) \big]\).

If \(g(x) \) is a non-constant function defined for all real values of \( x \), then what is the minimum number of distinct solutions \(f(x) = g(x) \) can possess?

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