(a) At what points are the functions and and differentiable? At what points are f and g and h holomorphic?

Using Cauchy-Riemann equations (+ showing continuity of partial derivatives) I have found:

f is differentiable only at

For g, solving for x and y in Cauchy-Riemann I end up with and so is in the form . Now, are continuous \{ } and since we must have \{ }. So, g should be differentiable \{ } satisfying .

But I have read that polynomial with coefficients in are differentiable in . Hence, I'm not sure about my answer for g.

h is differentiable only at

As to where the functions are holomorphic, I'm not quite sure I understand the concept very well. What I have found:

f and h are nowhere holomorphic.

if my answer for the first part is right, then g is holomorphic in and . But now that I think of it it doesn't really make much sense.

Can someone please check these answers for me?