Let f,g ∈ L∞[a, b] and c ∈ R. a) Show that cf ∈ L∞[a, b]. b) Show that f + g ∈ L∞[a, b].

f: X→ Y and g: Y→ V be bijective functions. Show the following: ) gof: XV is injective. ) gof: X→ V is surjective. (gof)-¹f-¹ og ¹ =

The function f:P (₂)→X" for X is a two-element set (0,1) is?. a) Bijective b) Surjective c) Injective d) No injective Answer OO A B 8. OC O

c) Let the set A = {-1,0, 1} and consider the following function: f3 A × A → A × A given by f(x,y) = (y7,x). Decide whether this function is injective, surjective, a bijection. f3 is an injection: Not Answered • ƒ3 is a surjection: Not Answered f3 is a bijection: Not Answered d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following function: f₁ : P(A) → P(A) given by ƒ(B) = {1, 2, 3}\B. Decide whether this function is injective, surjective, a bijection. f4 is an injection: Not Answered f4 is a surjection: Not Answered • f is a bijection: Not Answered