Let the function f of.... | JEE Advanced 2024 | Monotonicity

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Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)} $$ Then the number of solutions of $f(x)=0$ in $R$ is

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