Question

What is the domain and range of the square root of x+3-1?

Answer 1

`\large\boxed{\text{The domain:}\ x\geq-3\to x\in[-3,\ \infty)}\\\boxed{\text{The range:}\ y\geq-1\to y\in[-1,\ \infty)}`

Explanation:

`y=√(x+3)-1\\\\The\ domain:\\\\x+3\geq0\qquad\text{subtract 3 from both sides}\\\\x\geq-3\to x\in[-3,\ \infty)\\\\The\ range:\\\\√(x+3)\geq0\qquad\text{subtract 1 from both sides}\\\\√(x+3)-1\geq-1\\\\y\geq-1\to y\in[-1,\ \infty)`