Verified answer

The number under the square root must be positive

In this case,

x - 5 > 0

x > 5

domain: [5, infinity)

Ok, so the domain is referring to x values. To find the domain, you need to find the restrictions on the equation. In other words, what can't x be? You know that the square root of a negative number results in imaginary values, so therefore x can't be less than 5. Remember to take into account that x could be 5 because 5-5=0 and yes, you can take the square root of 0.

The domain is x is greater than or equal to 5. If you need to write that in interval notation, it would be [5, pos. infinity). (You would need a bracket on 5 because it is included. If you're in REGULAR algebra, I don't think you need to know that)... ;)

I hope I've been a good online math tutor to you.

Basically what would make a negative under the radical? Anything less than 5, so x is defined on 5<x<infinity (x can also equal 5 but I dont know how to make that sign)

The previous answer was correct. Just a side note, infinity is not usually considered inclusive. The domain should be written as [5, infinity) to avoid losing points on a technicality.

f(x) exist if:

x-5>or=0

set: x-5=0

or x=5

for x belongs to ]-infinity, 5 ] , f(x) do not exist .

and

f(x) exist,

for x belongs to [5 , +infinity[