Find the domain

• Apr 10th 2010, 03:11 AM
differentiate
Find the domain
Find the domain of
$log_e (x + \sqrt {x^2 +1})$

I think there is some trick to it
I had all real x values
but it seems too easy for a 2 mark question

any thoughts?

Thanks
• Apr 10th 2010, 03:46 AM
HallsofIvy
Quote:

Originally Posted by differentiate
Find the domain of
$log_e (x + \sqrt {x^2 +1})$

I think there is some trick to it
I had all real x values
but it seems too easy for a 2 mark question

any thoughts?

Thanks

That's exactly right. $x^2> 0$ for all x so $x^2+ 1> 1$ and $\sqrt{x^2+ 1}>\sqrt{x^2}> |x|$. For all x, $x+ \sqrt{x^2+ 1}> 0$ so the domain is all real numbers.