Lets say I have a function defined as $f(x) = \sqrt {x^2}$. Common knowledge of square roots tells you to simplify to $f(x) = x$ (we'll call that $g(x)$) which may be the same problem, but it isn't the same equation. For example, say I put $-1$ into them:

$\begin{align}
f(x) &amp;= \sqrt {x^2} \\
f(-1) &amp;= \sqrt {(-1)^2} \\
f(-1) &amp;= \sqrt {1} \\
f(-1) &amp;= 1
\end{align}$

$\begin{align}
g(x) &amp;= x \\
g(-1) &amp;= -1
\end{align}$

thereby, we conclude that $f(x)$ and $g(x)$ do not produce the same results even though they are mathematically the same. This is also shown when we try to graph the functions:

$y = \sqrt {x^2}$:



$y = x$:



$y = \mid x \mid$:



From this, we can see that given $f(x) = \sqrt {x^2}$, when simplified is not the same as $f(x) = x$. So, is there any way to prove that $y = \sqrt {x^2}$ is not the same as $y = x$ for negative values, but is infact the same as $y = \mid x \mid$?


Question: From installed file ,how to find which msi would have installed the file?
Answer: There's no guarantee that an MSI installed the file.  That said, one quick hack that I've used a lot is the ms-dos findstr command

On a machine with the config files installed:

CD %WINDIR%\Installer
FINDSTR -i -m dark.exe *.msi *.msi


This will do a case insensitive search of across all MSI files for the string dark.exe.   Then use ORCA to inspect the resultant MSI(s) to see if the hit is accurate and what product it is.  Reminder: The MSI name will be some short hex hash as these are the stripped / cached MSI's not the original MSI's.