# Use of $\arg$ function [closed]

I know that $\underset{x}{\operatorname{argmax}}f(x)$ is defined as the value at which $f(x)$ has its maximum. There is also $\underset{x}{\operatorname{argmin}}$.

However, in statistics, I often write something like $\Phi(z)=0.95$, and I am then looking for the value z that satisfies the equation.

Thus, this seems like something as $\underset{z, \textrm{where} f(z)=0.95}{\operatorname{argspecificvalue}}f(z)$.

Does something like that exist, i.e. how can I define the value z that satisfies the equation and how would one write it?

## closed as unclear what you're asking by John B, Ferra, Wojowu, Frits Veerman, Daniel W. FarlowMay 9 '16 at 12:08

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

There could be more such values. What you are looking for is to determine the set $$\Phi^{-1}(0.95) = \{ z : \Phi(z) = 0.95 \}$$ It is called the inverse image of $0.95$ under $\Phi$.