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There are some problems that ask you to find an equation with some information and I'm having trouble with it

For example, z= F(x,y) = -(y/x)^2 + h(xy), for some arbitrary function h.

They give you the condition that F(1,y) = y^2, and to find z now.

So with obvious substitution you get h(y) = 0

But how does that tell you anything else about z?

Does it mean h(t) = (t - y) ? Aren't there an infinite amount of ways to express h anyway (like ln(t-y+1) for example)? I doubt they are asking you for an explicit form, since no other information is available, but how do you go about solving a problem like this. I'm having a little problems understanding what exactly it's saying.

Does h(y)=0 mean y is a solution to the function h when the domain is restricted to points (1,y)?

For example, z= F(x,y) = -(y/x)^2 + h(xy), for some arbitrary function h.

They give you the condition that F(1,y) = y^2, and to find z now.

So with obvious substitution you get h(y) = 0

But how does that tell you anything else about z?

Does it mean h(t) = (t - y) ? Aren't there an infinite amount of ways to express h anyway (like ln(t-y+1) for example)? I doubt they are asking you for an explicit form, since no other information is available, but how do you go about solving a problem like this. I'm having a little problems understanding what exactly it's saying.

Does h(y)=0 mean y is a solution to the function h when the domain is restricted to points (1,y)?

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