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

2 Answers
Aug 17, 2017

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.

Aug 17, 2017

[-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)