Question

Hey! I need to know the domain of this, thanks!

Answer 1

`\sqrt x` is defined for
`x\ge0`. This means
`√(x+3)` exists only for
`x+3\ge0`, or
`x\ge-3`; and
`√(5-x)` exists for
`5-x\ge0`, or
`x\le5`. We can't divide by 0, so we have to exclude
`x=0` from the domain.

So the domain of
`f(x)` is
`[-3,5]\setminus\{0\}`, or
`[-3,0)\cup(0,5]`.