How do you find the domain and range of $f(x,y) = sqrt(9-x^2-y^2)$ ?

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Answer 1 · 2017-04-07T04:06:19

D: $-3<=x<=3$
R: $-3<=y<=3$

For the function:

$f(x,y)=sqrt(9-x^2-y^2)$

What is the list of allowable $x$ values - the domain?

We can't have a value under the square root sign that is less than 0, and so we can see that with $-3<=x<=3$ we have acceptable values.

What then is the resulting values of $y$ - the range?

With $x=-3, y=0$
With $x=0, y=pm3$
With $x=3, y=0$

And so the range is $-3<=y<=3$

How do you find the domain and range of f(x,y) = sqrt(9-x^2-y^2)f(x,y) = sqrt(9-x^2-y^2)?