Sign Analysis of irrational functions

[mcfaker]

Hi, I am from Belgium so i apologize for my English,
I have encountered a problem, i don't understand how to set up the sign analysis of irrational functions, so i decided to find some information on the internet, but the problem is that I am not sure if "sign analysis of irrational functions" is correct to type into google? "

Thank you very much.

 

[HallsofIvy]

The problem is that I don't know what you mean by "sign analysis of irprational functions" and neither does google! When I entered that, I got exactly one hit- this page!

On the other hand, when I first misread your post and entered "sign analysis of rational functions" or just "sign analysis", I got a number of hits. Are you sure you want irrational functions (such as square roots, etc.) rather than rational functions (fractions of polynomials)?

 

[mcfaker]

Here's an example of what i mean:

Is this correct English ( Sign analysis of irrational functions)?

 

[arildno]

Hi, mcfaker!
What you need to remember is that such an expression will have a LIMITED DOMAIN, namely those regions where either of the radicands are negative.

The overall sign of f(x) will be..positive.

Thus, let us look at your denominator.

In which regions are your two factors same-signed?

Clearly, this occurs in (-4,3), and no other open interval!
Other values for x are therefore inadmissible, and do not belong to the domain of f!

Now, for your numerator:
The (x-1)^2 factor can be ignored as yet, since it is always non-negative.

We see that the product 2*(x+2)*(x-5) are positive in the regions (-inf,-2) and in (5,inf)
The region (-2,5) is therefore a forbidden domain for f!

Therefore, the only region on the whole line that can be the domain of f, is the half-open interval (-4,-2]