# How do you find the domain of #f(x)=sqrt(1/2x-10)+3#?

##### 2 Answers

The domain is

#### Explanation:

The domain is determined of what's under the square root sign.

Therefore the domain of

#### Explanation:

The domain of a real function of real variable is the subset of the real numbers formed by those numbers for which the image exists:

This assumes, in order to obtain the domain of the function, that when a function's formula only contains internal operations in

The square root is a non-internal operation in

So to know when the radicand is positive or negative, what we do is equate to zero:

and then we can define the domain of

To solve the domain of the function above:

we must equal zero the term inside the root:

and solve the equation obtained:

It is easy to see that if