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 [math]x>-\frac{1}{2}\quad \text{or}\quad \left(-\frac{1}{2},\infty\right)[/math]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 [imath]1-x^2\ne0[/imath]
[imath]\therefore[/imath] The domain is [imath] (-\tfrac{1}{2},\infty) \setminus \{1\}[/imath]