# Math Help - Finding Domain of a function

1. ## Finding Domain of a function

Find the domain of the function f(x,y) = square root(y) + square root(25-x^2 - y^2)

square root(y) is defined only when y equal or > then 0.
square root(25-x^2 - y^2) is defined only when 25> or equal to x^2+y^2

so the domain of f is {(x,y) | y>,eqaul to 0, x^2+y^2<,equal to 25}

Did I make a mistake here?

2. To simplify the description of the domain, we may note that

$x^2+y^2=5^2$

is the equation of a circle of radius $5$ in the $xy$-plane centered at the origin.

3. so how does that change my domain i had written? I dont understand

4. Originally Posted by andreaspohle
so how does that change my domain i had written? I dont understand
It doesn't change it; it simply makes it easier to "see", that the domain of the function is the "top half" (in the first and second quadrants) of the circle of radius 5 centered at (0,0).