Gaokao Math Practice Question

设 $a \in \mathbf{R}$, 函数 $f(x)=\left\{\begin{array}{ll}\cos (2 \pi x-2 \pi a) . & x<a \\ x^{2}-2(a+1) x+a^{2}+5, & x \geq a\end{array}\right.$, 若 $f(x)$ 在区间 $(0,+\infty)$ 内 恰有 6 个零点, 则 $a$ 的取值范围是 ($\quad$)

1. A.$\left(2, \frac{9}{4}\right] \cup\left(\frac{5}{2}, \frac{11}{4}\right]$
2. B.$\left(\frac{7}{4}, 2\right) \cup\left(\frac{5}{2}, \frac{11}{4}\right)$
3. C.$\left(2, \frac{9}{4}\right] \cup\left[\frac{11}{4}, 3\right)$
4. D.$\left(\frac{7}{4}, 2\right) \cup\left[\frac{11}{4}, 3\right)$