# For which pairs of numbers (x.y) is the function given below defined?

## ${\left({x}^{2} + {y}^{2}\right)}^{\frac{1}{2}} + {\left({x}^{2} + {y}^{2} - 1\right)}^{\frac{1}{2}}$

for ${x}^{2} + {y}^{2} \ge 1$
$\left({x}^{2} + {y}^{2} - 1\right)$ should be positive and if it is, (${x}^{2} + {y}^{2}$ )will be positive too
therefore, this function will be defined for all ${x}^{2} + {y}^{2} \ge 1$