# Find and Sketch the Domain of a Function

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1. Feb 15, 2016

### cosmos42

1. The problem statement, all variables and given/known data
ƒ(x,y) = √y + √[25-x2-y2]

2. Relevant equations

3. The attempt at a solution
The expression for f(x,y) is defined as long as x2 + y2 ≥ 25 and y ≥ 0 because of the square roots we can't have negative numbers. {(x,y) ∈ ℝ2 : y ≥ 0 and x2 + y2 ≥ 25} I'm not sure how I'd represent it graphically.

2. Feb 15, 2016

### andrewkirk

What is the shape of the region of the number plane that satisfies $x^2+y^2\leq 25$?
What is the shape of the region of the number plane that satisfies $y\geq 0$?
What is the shape of the intersection of those two regions?