Multivariable Calculus help?

Each transformation is continuously differentiable (C1) on its domain -- R^2, or R^2∖{(0,0)} for the function involving log -- so Inverse Function Theorem implies it has a C1

inverse near every point satisfying some conditions. Match each transformation with the set of points in its domain that DO NOT satisfy the conditions.

 1. f(x,y)=(xe^(x^2+y^2),ye^(x^2+y^2))

 2. f(x,y)=(e^(x+3y),xy+y^2)

 3. f(x,y)=(x/(e^(x^2+y^2)),y/(e^(x^2+y^2)))

 4. f(x,y)=(xlog(x^2+y^2),ylog(x^2+y^2))

 5. f(x,y)=(x^3,y^3)

A. the line y=x

B. the line y=−x

C. the x and y axes

D. the empty set

E. the circle 2x^2+2y^2=1

F. the circle (ex)^2+(ey)^2=1 and the origin

G. the origin

H. the circle (ex)^2+(ey)^2=1

I really don't understand how to do this problem, can someone please help and explain it??