What is the domain of this function?

[itsrayex]

That was my canclusion but its wrong because apparently this is the result:

Can you please tell me why?

 

[BigBeachBanana]

From your domain for the log function, you showed that $$x>-\frac{1}{2}\quad \text{or}\quad \left(-\frac{1}{2},\infty\right)$$Since -1 is not in the set, there's no need to remove it from the set.

 

[lex]

Your solution is the same as theirs although the notation of your final answer is not exactly correct.

For the top line of the function to exist, we simply require 2+4x>0
For the division to exist we require $1-x^2\ne0$
$\therefore$ The domain is $(-\tfrac{1}{2},\infty) \setminus \{1\}$