Question

How do I find the domain of the function `f(x)=sqrt(x+8)`?

Answer 1

Domain: all Real `x` such that `x>=-8`

Explanation:

The domain will be the set of `x` values that are accepted by your function (and return a value).
In this case we have to be careful because in case of a negative argument of the square root we will be in trouble.
To eliminate this possibility we say that the domain will be the set of `x` values such that the argument of the root is bigger or equal to zero (so that our function can return us a value) or:

`x+8>=0`

giving that:

`x>=-8`

So, as long as `x` remains equal or bigger than `-8` it is all right.

Answer 2

`[-8, oo)`

Explanation:

Set the expression under the square root greater or equal to zero:

`x+8 >= 0`

Solve the equation:

`x>= -8`

Write the answer using interval notation:

`[-8, oo)`