Question

Find and sketch the domain of f(X,y) = 1/√x^2-y

Answer 1

Explanation:

The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function

The function given is
`F(x, y)=(1)/(√(x^2-y) )` , the denominator cannot be 0.
So we set up the equation

`√(x^2-y) \\eq 0`

`√(x^2-y)^(2) \\eq 0x^2-y\\eq 0x^2\\eq y`

And that the the square root needs to be more than 0.

`√(x^2-y)\geq 0`

`x^2-y\geq 0`

`x^2\geq y`

So we can conclude that all values of
`x^(2)` must be greater y

That means that our domain is all X values greater than
`√(y)`