Find the domain of `f(x)=sqrt(x+9)` :
The domain of a function is the set of all possible inputs.
For most functions the domain is all real numbers -- however in the real numbers we cannot divide by zero, take an even root of a negative number, or take a logarithm of a nonpositive argument.
For f(x) we must insure that the radicand is nonnegative.
`x+9gt=0 ==gt xgt=-9`
The domain is `x>=-9` .
Since the given function contains square root, we are required to find the values of x that will make the radicand (or the value inside the radical symbol) positive. This gives us
In other words, the domain or the solution of the function is the set of real numbers greater than or equal to -9. When written in interval form, the domain will be