What is the domain of f(x)=sqrtx+9?

2 Answers

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

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` .

The graph:

kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

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