# How do you find the domain and range of #f(x) = (2x)/(sqrt(16-8x))#?

##### 1 Answer

**Domain:**

The domain will be determined by saying that the radical has to be *larger* than

Consider the function

The domain would be

Now consider the function

Recall that a square root is undefined in the real number system if the number inside the square (the radicand) is less than 0 (**cannot** be equal to

Back to our function at hand:

Hence, the domain is

The graph of the function, shown in the following image, justifies our answer.

**Range:**

From as far as I can tell, the range is all the real numbers. I looked at the graph to huge numbers (ex.

Thus, the range is

**In summary:**

For the function

•The domain is

•The range is

**Practice Exercises:**

Determine the domain and range of the function

Hopefully this helps, and good luck!