Question

How would you find the domain of the function: f(x)= (sqrt x+2) / (10-x)
Must be in interval notation.

Answer 1

First, it's not clear. Is it \(\sqrt{x+2}\;or\;\sqrt{x}+2\) in the numerator?

Answer 2

\[\sqrt{x+2}\]

Answer 3

Okay, start with "All Real Numbers" and throw out the bad guys. What Real Numbers don't work. What situations cause problems?

Answer 4

\[\frac{ \sqrt{x+2} }{ 10-x }\]

Answer 5

Denominators can be a problem. Why?
Square roots can be a problem. Why?