Reference no: EM132381000
Functions Problems -
Problem 1 - Show that if f is bijective, an inverse g of f exists, i.e., define such a g, show that it is a function, and show that it is an inverse of f , i.e., f (g(y)) = y and g(f(x)) = x for all x ∈ X and y ∈ Y.
Problem 2 - Show that if f : X → Y has an inverse g, then f is bijective.
Problem 3 - Show that if g : Y → X and g' : Y → X are inverses of f : X → Y, then g = g', i.e., for all y ∈ Y, g(y) = g'(y).
Problem 4 - Show that if f : X → Y and g : Y → Z are both injective, then g o f : X → Z is injective.
Problem 5 - Show that if f : X → Y and g : Y → Z are both surjective, then g o f : X → Z is surjective.
Problem 6 - Given f : X 
Y, define the partial function g : Y X by: for any y ∈ Y, if there is a unique x ∈ X such that f(x) = y, then g(y) = x; otherwise g(y) ↑. Show that if f is injective, then g(f(x)) = x for all x ∈ dom(f), and f(g(y)) = y for all y ∈ ran(f).
Problem 7 - Suppose f : X → Y and g : Y → Z. Show that the graph of (g o f ) is Rf | Rg.
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Journal entries required to adjust the cash account at nov
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What does voltaire mean by the phrase cultivate our garden
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Case study - southern cross healthcare
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Define the partial function
: Functions Problem- Show that if f is bijective, an inverse g of f exists, i.e., define such a g, show that it is a function, and show that it is an inverse of f
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