Hi, thanks.

Let's just ignore g(x) for now.

I'm aware that f(-1) is undefined, but what I'm saying is that I can algebraically manipulate

to make

by the above process.

The problem is that in doing so, it seems the domain of the function "changes". There is no

such that

is undefined.

Or, do we have to keep the domain of

fixed, so even though I manipulate it, the domain stays the same so even though

, we have said that we can't allow x to take the value -1?

By that logic, I can algebraically manipulate

by:

But in this case, I could have orignally defined the domain of f for all real numbers! In both cases, the domain changes. What's the story?