Question

23. (a) Show that a function f : X → Y is a surjection if and only if there is a funct io On g : Y → X such that fog = idy. (b) Show that a function : X → Y with nonempty domain X is an injection if and only if there is a function g : Y → X such that g o f-idx. How does this result break down if X = φ? (c) Show that f : X → y is a bijection if and only if f has an inverse function. (d) Consider a function f : X → y. Suppose g : Y → X is an inverse of the function f, and suppose h : Y → X is also an inverse of the function f. Prove that g = h. Continuous Functions u look over the example of bijections functions did better than others at preserving the integrity of their domains. For let although the hilection ton . / ππ) you may notice that -

Answer 1

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