7. Given that $f(x)$ and $g(x)$ are odd functions, the solution set for $f(x)>0$ is $\left(a^{2}, b\right)$, and the solution set for $g(x)>0$ is $\left(\frac{a^{2}}{2}, \frac{b}{2}\right)$ (where $a, b$ are constants, and $b>2 a^{2}$). Then the solution set for $f(x) \cdot g(x)>0$ is
A. $\left(\frac{a^{2}}{2}, b\right)$
B. $\left(-\frac{b}{2},-a^{2}\right) \cup\left(a^{2}, \frac{b}{2}\right)$
C. $\left(\frac{a^{2}}{2}, b\right)$
D. $\left(\frac{b}{2}, b\right)$
7. B Because $f(x) \cdot g(x)$ is an even function, its graph is symmetric about the $y$-axis. Therefore, the solution set of $f(x) \cdot g(x)>0$ must be a symmetric interval. Choose B.