What is the domain of $f(x,y)= arcsin(x^2+y^2-5)Ln(x+2y+1)$ ?

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Answer 1 · 2016-08-11T14:36:21

$-1 le x^2+y^2-5 nn x^2+y^2-5 le 1 nn x + 2y + 1 > 0$

The feasible region for $f(x,y)= arcsin(x^2+y^2-5)Ln(x+2y+1)$ is given by

$-1 le x^2+y^2-5 nn x^2+y^2-5 le 1 nn x + 2y + 1 > 0$

which corresponds to the region plotted in light blue.

enter image source here

What is the domain of f(x,y)= arcsin(x^2+y^2-5)Ln(x+2y+1)f(x,y)= arcsin(x^2+y^2-5)Ln(x+2y+1)?