notes/education/math/Domain.md

Examples

Given the below problem, the two equations can't simplified further. So to find the domain, you need to look for the domain where they're both valid, eg [-2, 5].

 \sqrt{x+2} + \sqrt{5-x} 

The below example has a domain of [-2, 5) because x cannot equal 0 for the denominator

 \frac{\sqrt{x+2}}{\sqrt{5-x}} 

Assuming f(x) = \frac{2}{x-3}, and g(x) = \frac{5}{x+1}, (f\circ g)(x), you can find the domain by finding the domain for each function, then fully expanding it and seeing if any more unreachable numbers are included