Find the domain of
$\displaystyle log_e (x + \sqrt {x^2 +1})$
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. $\displaystyle x^2> 0$ for all x so $\displaystyle x^2+ 1> 1$ and $\displaystyle \sqrt{x^2+ 1}>\sqrt{x^2}> |x|$. For all x, $\displaystyle x+ \sqrt{x^2+ 1}> 0$ so the domain is all real numbers.