Question

Find and sketch the domain of the function \(f(x,y) = \sqrt y + \sqrt {25 - {x^2} - {y^2}} \)

Short answer

The domain of the function is \(\left\{ {(x,y)/y \ge 0;{x^2} + {y^2} \le {5^2}} \right\}\)

Step-by-step solution

Step 1:- Consideration

Let \(f(x,y) = \sqrt y + \sqrt {25 - {x^2} - {y^2}} \) is a function

Finding Relation

For the function to be real it must be grater than or equal to zero i.e.

Graph

Hence, the domain of f is \(\left\{ {(x,y)/y \ge 0;{x^2} + {y^2} \le {5^2},y \ge 0} \right\}\)