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

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embizze's profile pic

embizze | High School Teacher | (Level 1) 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

`x+9gt=0`

`xgt=-9`

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

`[-9,oo)`

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