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

Answer:

Domain is the half closed interval

$[-2,\infty)$

Step-by-step explanation:

Given is a function

$y=\sqrt{4x+8}$

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

$[-2,\infty)$