Let\( f(x) = \sin(x) \) and \(g(x) = x^2 - 2 \) for \(x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \) . Then, which of the following holds?
1
\(f(x) \geq g(x) \) for all\( x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \)
2
\(f(x) \leq g(x) \) for all \(x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \)
3
f(x) - g(x) changes sign exactly once on \(\left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \)
4
f(x) - g(x) changes sign more than once on \(\left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \)