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

**True or False**

If \( g(x) = 0 \) for all values of \(x\), then \(f(x) = 0\) has finitely many solutions.

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