Question

Find the Domain of each expression

Answer 1

`-1 \le x\le1.5`

Explanation:

The expression we're given, we want both to be defined because how can you add a defined number to an undefined number?

Square roots only have real solutions for positive numbers and zero

So let's set up an inequality for both square roots

`2x+2\ge0\\\\6-4x\ge0`

Let's solve the first one

`2x+2\ge 0\\2x\ge-2\\x\ge-1`

this is the domain of the "first expression"

let's solve the second one

`6-4x\ge 0\\-4x\ge -6\\x\le 1.5`

We want them to overlap, so we get a compound inequality:
`-1 \le x\le1.5`

since we want both of the expressions to be defined to define the entire thing.