Consider function f: R R defined by f(x) = [x] , that is, the floor...

 

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Consider function f: R → R defined by f(x) = [x] , that is, the "floor function" defined by x, if x is an integer [x] = largest integer smaller than x, otherwise and consider function g: R+ → R† defined by g(x) : = Vx (a) Determine the image of function f (2 Marks) (b) Is function f a bijection? If yes, prove it. If not, justify why not. (5 Marks) (c) Determine the image of function f•g (2 Marks) (d) cardinality as the set of all natural numbers. Prove that the set of all odd natural numbers has the same (8 Marks) Consider function f: R → R defined by f(x) = [x] , that is, the "floor function" defined by x, if x is an integer [x] = largest integer smaller than x, otherwise and consider function g: R+ → R† defined by g(x) : = Vx (a) Determine the image of function f (2 Marks) (b) Is function f a bijection? If yes, prove it. If not, justify why not. (5 Marks) (c) Determine the image of function f•g (2 Marks) (d) cardinality as the set of all natural numbers. Prove that the set of all odd natural numbers has the same (8 Marks)