Given the following function with two variables: \begin{equation} \frac{\sqrt{4x-x^2-y^2}}{x^2y^2-4xy^2+3y^2} \end{equation} I need to find a) the domain for the above function. Can anyone give me a hint on how to find the domain in f?
I already know that: \begin{equation} dom f = \{ f(x,y) ∈ \mathbb{R}^2\backslash(x^2y^2-4xy^2+3y^2=0) : \sqrt{4x-x^2-y^2} \geq 0 \} \end{equation} But of course this needs to be written in a more simpler form. During class we solve simpler functions like without fractions and roots, so I don't have anything that can help me.
After this I also need to find:
- b) zeros of the function
- c) Calculating Algebraically, the range of the function: \begin{equation} T(x,y) = \sqrt{4x-x^2-y^2} \end{equation}
- d) Extreme values of the function T
I'm of course not expecting the complete solution but something like a kick start.