已知函数 $f(x)=\left\{\begin{array}{c}-\frac{1}{4} x+a, x \leq 2 \\ \log _a x, x>2\end{array}\right.$, 若命题 " $\exists x \in \mathbf{R}, f(x) < 1$ "为假命题, 则实数 $a$ 的取值范围是
A
$\left[\frac{3}{2}, 2\right]$
B
$(1,2]$
C
$(1, \sqrt{2}]$
D
$\left[\sqrt{2}, \frac{3}{2}\right]$
E
F