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

##### 1 Answer
Aug 11, 2016

$- 1 \le {x}^{2} + {y}^{2} - 5 \cap {x}^{2} + {y}^{2} - 5 \le 1 \cap x + 2 y + 1 > 0$

#### Explanation:

The feasible region for $f \left(x , y\right) = \arcsin \left({x}^{2} + {y}^{2} - 5\right) L n \left(x + 2 y + 1\right)$ is given by

$- 1 \le {x}^{2} + {y}^{2} - 5 \cap {x}^{2} + {y}^{2} - 5 \le 1 \cap x + 2 y + 1 > 0$

which corresponds to the region plotted in light blue.