Given the following functions, determine their domain and graph the domains:
a) $ f (x, y) = \sqrt {| x | - | y |} $
b) $ f (x, y) = \log (1- 4x ^ 2 - \frac {x ^ 2} {9}) $
c) $ f (x, y) = \sqrt {(x-3) \cdot (y-2)} $
d) $ f (x, y) = \sqrt {\frac {4- x ^ 2-y ^ 2} {x ^ 2 + y ^ 2-1}} $
Is there a mechanical way for me to resolve these issues? It is really a doubt. Is there a program that makes me better understand, or do I need to do it manually?
Basically what you need to know is that anything inside a square root is non-negative, so for the first case for example, you should have $|x| \geq |y|$. Can you graph this?
C) and D) require similar analysis.
For the case B), you need to know that anything inside a logarithm is positive. That is, for $y= \log x$, the domain of $x$ is greater than $0$. Can you proceed ahead?