The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Set the radicand in √x−9 greater than or equal to 0 to find where the expression is defined. Add 9 to both sides of the inequality. The domain is all values of x that make the expression defined. The range of an even indexed radical starts at its starting point (9,0) and extends to infinity.

0 to ∞

The natural domain is sometimes called the maximum domain; it is often simply called the domain of the function. For example: The function y=1x has domain {x∈R∣x≠0}, which is also written as R∖{0}.

1 Answer. It is for every value in the domain. Notice, 0 is not in the domain of neither f(x)=1x nor f′(x)=1×2. Looking at the plot of f(x), we see on the negative side of the domain, the function is always decreasing, and on the positive side, the function is always decreasing.

The domain is how much the function takes x-wise, in the horizontal axis. As y=−1 is a horizontal line at y=−1 , horizontally-wise it takes all real numbers, from −∞ to +∞ Therefore, the domain is ℝ.

How To: Given a function written in equation form including an even root, find the domain.

1. Identify the input values.
2. Since there is an even root, exclude any real numbers that result in a negative number in the radicand.
3. The solution(s) are the domain of the function.

The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

The domain of the function y=cot(x)=cos(x)sin(x) is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n . The range of the function is all real numbers.