Question

Is domain of f(x,y) = 1 + (4 -y^2)^1/2 open, closed or neither

is it bounded or unbounded?

Answer 1

Closed and Bounded.

Explanation:

Hi there!

1) Let's start by finding the values in which the function is defined. Remember that this can be rewritten:

`f(x,y) = 1 + (4 -y^2)^{(1)/(2)} \:id\:est\:f(x,y)=1+√((4 -y^2))`

Since every quadratic root are defined for values
`\geq` 0 then, this help us to understand that we need calculate what interval this Domain is:

`4-y^(2) \geq 0\\4-y^(2)-4\geq -4\\-y^(2)\geq-4 \\y^(2)\leq4\\-2\leq y\leq 2`

`D=[-2,2]`

2) Graphically speaking, the domain is closed. For the values -2 and 2 are included, and bounded.

Bounded functions have all of their points contained by some circle origin centered. Check it out below.