Optimization related to CDF of standard normal distribution

Question

Let $g(x) = (\mathbb{P}(Z>f(x)))^2$, where $Z$ follows standard normal distribution. Is it true that $g(x)$ maximizes at $x_0$ where $x_0 = \operatorname{argmin} f(x)$?

Answer 1

It is evident that $g(x)$ will reach maximal value where $\mathbb P(Z>f(x))$ will reach maximal value.

Also it is evident that $\mathbb P(Z>f(x))$ will reach maximal value where $f(x)$ will reach minimal value.