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Mathematics
Mathematics
Problem
Let the function
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be defined by
f
(
x
)
=
sin
x
(
x
2023
+
2024
x
+
2025
)
e
π
x
(
x
2
−
x
+
3
)
+
2
(
x
2023
+
2024
x
+
2025
)
e
π
x
(
x
2
−
x
+
3
)
.
f(x) = \frac{\sin x (x^{2023} + 2024x + 2025)}{e^{\pi x} (x^2 - x + 3)} + \frac{2 (x^{2023} + 2024x + 2025)}{e^{\pi x} (x^2 - x + 3)}.
f
(
x
)
=
e
π
x
(
x
2
−
x
+
3
)
sin
x
(
x
2023
+
2024
x
+
2025
)
+
e
π
x
(
x
2
−
x
+
3
)
2
(
x
2023
+
2024
x
+
2025
)
.
Then the number of solutions of
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
in
R
\mathbb{R}
R
is \_\_\_\_\_\_.
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