Question

What is the domain of the function y=
`\sqrt{x+6-7`

Answer 1

If the function is
`y=√(x+6) -7` , the domain are all values of x greater than or equal to -6

If the function is
`y=√(x+6-7)` , the domain are all values of x greater than or equal to 1

Explanation:

First case

we have

`y=√(x+6) -7`

we know that

The radicand of the function must be greater than or equal to zero

so

`x+6 \geq 0`

`x\geq-6`

the solution is the interval---------> [-6,∞)

therefore

The domain are all values of x greater than or equal to -6

Second case

we have

`y=√(x+6-7)`

so

`y=√(x-1)`

we know that

The radicand of the function must be greater than or equal to zero

so

`x-1 \geq 0`

`x\geq 1`

the solution is the interval---------> [1,∞)

therefore

The domain are all values of x greater than or equal 1