Range and Domain of a function

[Guest]

Hello!

Im a regular student and Math is a really difficult topic for me, and every once in a while i run into a problem that i am unable to solve. This time i would like to ask this community for some help. Many thanks in advance.

The function itself is: y = sqrt((x^2-5*x+6)/log[10]((x+10)^2))

I was able to determine the domain (X), but i am having very big trouble with finding the range (Y). Also i should be able to do it with pen on paper, but so far i have wasted 2 days and many papers on pointless scribblig.

Could anyone please explain how could i find the range of that function and provide a step by step solution?

[Guest]

The range is all values [tex][0,\infty)[/tex].

At [tex]x = 3[/tex] the value is [tex]0[/tex] as [tex]x[/tex] increases the value increases to infinity, since the function is continuous it must attain all values between [tex]0[/tex] and [tex]\infty[/tex]. Since the function uses a square root the range can only consist of non-negative values, so the range must be [tex][0,\infty)[/tex].

Hope this helped,

R. Baber.