Please show detailed work for part (b) only. The answer has already been given for part (a).

Given answer for part (a): the function f₃(x, y) = y best represents the divegence, and the function f₁(x, y) = x best represents the (scalar) curl.

(1) Consider the following functions on R2: (1) f1 (x, y) = x, (ii) f2 (x, y) = -x, (iii) f3 ( x, y) = y, (iv) fa (x, y) = -y, (v) f5 ( x, y) = xty, (vi) fo (x, y) = x - y, (vii) f7 (x, y) = -xty, (viii) f8 (x, y) = -x- y.(a) Which of those functions best represent the divergence and the (scalar) curl of the vector field F : R2 - R2 depicted below? Justify your answer. 30 20 10 -10 -20 -30 -30 -20 -10 0 10 20 30(b) Come up with a concrete example of a vector field F : R - R matching your answer in (a)