Problem 1 (2 marks). A function f: R" -> R is called weakly increasing if f (x) > f(y) whenever x _ y. It is called strictly increasing if f (x) > f(y) whenever x > y. Finally, f is called strongly increasing if f (x) > f(y) whenever x 2 y, with x * y. Identify which property is satisfied in each of the following cases. Since the prob- lem is worth 2 marks, choose four out of the six cases. (a) Let f(x1, X2) = c1x1 + 2x2 defined on RR2 for c1, C2 > 0. (b) Let g(X1, x2) = In x1 + In x2 defined on R3. (c) Let do: RR2 - R. be the Euclidean distance to 0. (d) Let d2 : R" -> Ry be the Euclidean distance to z. (e) Let u( x1, X2) = x1 x72 defined on R4 , with a; > 0 for i = 1,2. (f) Let v(x1, x2) = min {x1, x2} defined on R3