# Math Help - describe the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3)

1. ## describe the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3)

hi,
the question asks for the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3).

which is z-x^2-y^2+2y+3 > 0.

when I try do describe the domain, all I get is 2 > x^2 + (y-1)^2 -z. I have no idea what the shape is like.

any ideas?

thx.

2. ## Re: describe the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3)

Originally Posted by sjjc1993
hi,
the question asks for the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3).

which is z-x^2-y^2+2y+3 > 0.

when I try do describe the domain, all I get is 2 > x^2 + (y-1)^2 -z. I have no idea what the shape is like.
Consider the surface

$z-x^2-y^2+2y+3=0.$

By completing the square, we have

$z+4=x^2+(y-1)^2$

This is a circular paraboloid, centered at (0,1,-4). So $z+4>x^2+(y-1)^2$ would consist of all the points above the paraboloid.

3. ## Re: describe the domain of f(x,y,z)=ln(z-x^2-y^2+2y+3)

thanks a lot!