Question

What is the domain of the function? y=sqrt(4x+8)

Answer 1

Obviously (hopefully) a square root function cannot be negative.

Also, 4x-8 must be >= 0, otherwise the sqrt is undefined for the reals.

4x-8 >= 0

4x >= 8

x >= 2

Then the range is [0, inf)
The domain is [2, inf)

Answer 2

Domain is the half closed interval

`[-2,\infty)`

Explanation:

Given is a function

`y=√(4x+8)`

We are to find the domain of the function

We see that a square root sign is there. This will be real only if

4x+8 is non negative

Hence condition for domain is

`4x+8\geq 0\\4x\geq -8`

We divide by 4 (a positive value) without disturbing inequality sign.

`x\geq -2`

Hence domain is

`[-2,\infty)`