suppose x is a real variable. what is the domain of the function [tex]\sqrt{{x-3}\over{x-1}}[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

here [tex]{{x-3} \over {x-1}} \geq 0[/tex]

from this we get the domain to be [tex]\left(-\infty, 1\right) \cup \left[3, \infty\right)[/tex]

but if we write the function [tex]\sqrt{{x-3}\over{x-1}} = \frac{\sqrt{x-3}}{\sqrt{x-1}}[/tex]

then [tex]x-3 \geq 0 \Rightarrow x \geq 3[/tex]

and [tex]x-1 > 0 \Rightarrow x > 1[/tex]

from these two, we get the domain [tex]\left[3, \infty\right)[/tex]

why do i get two different domains?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What is the domain of this function?

**Physics Forums | Science Articles, Homework Help, Discussion**