Question

y=Sqrt x-3 - sqrt x+3

Answer 1

\(\bf y = \sqrt{x-3}- \sqrt{x+3} \quad \large{or} \quad y = \sqrt{x}-3-\sqrt{x}+3\quad ?\)

Answer 2

the first one

Answer 3

h.... not sure you can simplify it further :|

Answer 4

Sorry, I forgot to mention that you need to find the domain.

Answer 5

the domain will be the values "x" can take without making either amount inside the radical negative

if x = 3, \(\bf \sqrt{x-3}\) becomes 0, if "x" becomes smaller than 3, then the value will turn negative, so "x" has to be +3 or bigger

if x = -3, \(\bf \sqrt{x+3}\) becomes 0, if "x" becomes smaller than 3, then the value will turn negative, so "x" has to be -3 or bigger

so in notation that'd be \(\bf x\ge 3 \qquad x \ge -3\)
but \(\bf x \ge 3\) cannot take values less than 3, like from -3 to +2
so the domain or values "x" can safely take are \(\color{purple}{\large \bf x \ge 3}\)