Question

Why can we multiply \[\sqrt{x-1}*\sqrt{x+1}=sqrt{x²-1}\]?
At first I thought it had to do with the domain but it is not the same...
\[dom \sqrt{x-1}=[1;+\infty)\]
\[dom \sqrt{x+1}=[-1;+\infty\]
\[dom \sqrt{x²-1}=(-\infty;-1]U[1;+\infty)\]

Answer 1

Fixed some displaying errors:

Why can we multiply \[\sqrt{x-1}*\sqrt{x+1}=\sqrt{x²-1}\]?
At first I thought it had to do with the domain but it is not the same...
\[dom \sqrt{x-1}=[1;+\infty)\]
\[dom \sqrt{x+1}=[-1;+\infty)\]
\[dom \sqrt{x²-1}=(-\infty;-1]U[1;+\infty)\]

Answer 2

ok so you can multiply
but the domain will be \([1,\infty)\)

Answer 3

Say I have example but the domain is mostly negative when multiplied (e.g. (-infty; 4])
does that mean I can still multiply but the domain for which the function is defined is [0;4]?

I don't really get when I can multiply and when not.

Answer 4

you can always multiply
just have to restrict the domain

Answer 5

Thank you