Let \(f:[0,3] \rightarrow\) A be defined by \(f(x)=2 x^3-15 x^2+36 x+7\) and \(g:[0, \infty) \rightarrow B\) be defined …

Let \(f:[0,3] \rightarrow\) A be defined by \(f(x)=2 x^3-15 x^2+36 x+7\) and \(g:[0, \infty) \rightarrow B\) be defined by \(\mathrm{g}(x)=\frac{x^{2025}}{x^{2025}+1}\). If both the functions are onto and \(\mathrm{S}=\{x \in \mathbf{Z}: x \in \mathrm{~A}\) or \(x \in B\}\), then \(\mathrm{n}(\mathrm{S})\) is equal to :

[JEE Main 2025, 28 Jan (Shift 2)]