Hello, I was having some trouble with this function here...

$\displaystyle \frac {log{|x^2-x+2|}}{\sqrt x}$

Domain:

We have an abs in the logarithm so all we need to do is the following:

$\displaystyle x^2-x+2 \ne 0$

$\displaystyle x >= 0$

$\displaystyle \sqrt x \ne 0$

The last two can be merged in... $\displaystyle x > 0$

The first one has no solution, means that I have no problem up there, so the domain is:

$\displaystyle (0;+ \infty)$

Now I have to study the signum...

$\displaystyle \frac {log{|x^2-x+2|}}{\sqrt x} >= 0$

I was used to distinguish the two cases and study two separate functions when I have the absolute value. But the stuff inside the absolute value is always positive, so the function with or without the absolute value is pretty much the same thing? So studying the function WITHOUT the abs, is the same thing? Thanks !