Hey there, I'm just trying to work out how to find the largest possible domain to the following function algebraically.

The way I've been going about it is:

must be greater than zero, so

must be greater than zero, so

and can't equal zero, meaning, for this part, can be any real number besides

From this I get the domain of

Which is not the complete domain stated in the answer. I must be missing something...

Thanks for your help