Question: Let \(f(x, y)\) be a function on \(\mathbb{R}^{2}\) with continuous partial derivatives up to order 2 , and consider \(g(r, \theta)\) defined by

1. Express the Laplacian of \(f\) :
   \[\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}\]
   in terms of the partial derivatives of \(g\).
2. Suppose that \(f(x, y)\) is an harmonic function (that is, its Laplacian is zero) of the form \(f(x, y)=h(r)\). Find all possible such \(f\).

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