I have two questions about convexity:

1)

f(x,y) is a convex function,

are the following functions convex too?

[f(x,y)]^{2}

ln[f(x,y)]

and

e^{[f(x,y)]}

I don`t really understand how to answer to this, in my opinion it is clear that they remain convex, but I'm not sure about the correct explaination why.

Secondly:

Is f(x,y)=ln(1-(x-a)^{2}-y^{2}) convex or concave?

"a" stands for a real number.

Can I simply perform the second derivative test on this?

So I set f`(x,y)=0 to get stationary points, than I take the second derivative and fill in the stationary points in order to test for convexity?