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.

Quote:

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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.

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Consider the surface



By completing the square, we have



This is a circular paraboloid, centered at (0,1,-4). So would consist of all the points above the paraboloid.

thanks a lot!