72 The increasing interval of the function $y=2\left(\log _{\frac{1}{2}} x\right)^{2}-2 \log _{\frac{1}{2}} x+1$ is
A. $\left(0, \frac{1}{2}\right)$
B. $\left[\frac{1}{2}, \frac{\sqrt{2}}{2}\right)$
C. $\left[\frac{\sqrt{2}}{2},+\infty\right)$
D. does not exist
72 C.
$$
y=2\left(\log _{\frac{1}{2}} x-\frac{1}{2}\right)^{2}+\frac{1}{2} .
$$

Since $\log _{\frac{1}{2}} x$ is a decreasing function, when
$$
\log _{\frac{1}{2}} x \in\left(-\infty, \frac{1}{2}\right]
$$

the original function is increasing. At this time, $x \in\left[\frac{\sqrt{2}}{2},+\infty\right)$.