[Optional 4-5: Inequalities] (10 points)
Given functions $f(x) = -x^2 + ax + 4$ and $g(x) = |x + 1| + |x - 1|$.
(2) If the solution set of the inequality $f(x) \geq g(x)$ contains $[-1, 1]$, find the range of values for $a$.

11. If the range of the function $f ( x ) = a \cdot \left( \frac { 1 } { 3 } \right) ^ { x } \left( \frac { 1 } { 2 } \leq x \leq 1 \right)$ is a subset of the range of the function $g ( x ) = \frac { x ^ { 2 } - 1 } { x ^ { 2 } + x + 1 } ( x \in \mathbb{R} )$, then the range of positive number $a$ is
A. $(0,2]$
B. $(0,1]$
C. $( 0,2 \sqrt { 3 } ]$
D. $( 0 , \sqrt { 3 } ]$

Let $S$ be the set of positive integral values of $a$ for which $\frac { a x ^ { 2 } + 2 a + 1 x + 9 a + 4 } { x ^ { 2 } - 8 x + 32 } < 0 , \quad \forall x \in \mathbb { R }$. Then, the number of elements in $S$ is:
(1) 1
(2) 0
(3) $\infty$
(4) 3

Let $a$ be a constant. Consider the quadratic inequality
$$x ^ { 2 } - 2 ( a + 2 ) x + 25 > 0 . \tag{1}$$
The left-hand side of inequality (1) can be transformed into
$$( x - a - \mathbf { A } ) ^ { 2 } - a ^ { 2 } - \mathbf { B } a + \mathbf { C D } .$$
Hence, we have the following results.
(1) The condition under which inequality (1) holds for all real numbers $x$ is
$$\mathbf { E F } < a < \mathbf { G } .$$
(2) The condition under which inequality (1) holds for all real numbers $x$ satisfying $x \geqq - 1$ is
$$\mathbf { H I J } < a < \mathbf { K } .$$