If f is a function having as its domain and range the set N of natural numbers, then f is bijective.

Let X-(1, 2, 3, 4, 5, 6). Define the functionf from P(X) to (0, 1] as the power set. What is f((2,5|)? O 020050 O 100100 O 01001 O 010010

Let f: A → B and g: B → C be functions. (a) Prove that if f : A → B is injective and g: B → C is injective, then go f is injective. (b) If f and go f are injective, is g always injective? Prove or provide a counterexample.

Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ______

Suppose f: R → R is a function from the set of real numbers to the same set with f(x) = x + 1. We write £ to represent fo f and fatl= fof. Is it true that £22o f = fo f?? Why? Is the set {g: R R | gof=fog} infinite? Why?

Prove that f is an identity function of itself.

Consider the set M = {0, 2, 4, 6} and N = {1, 3, 5, 7}. Determine if each of the following ordered pairs is a function with domain M and codomain N. If you state it is a function, then determine if it is one-to-one and/or onto. a. {(0,2), (2,4), (4,6), (6,0)} b. {(6,3), (2,1), (0,3), (4,5)} c. {(2,3), (4,7), (0,1), (6,5)} d. {(2,1), (4,5), (6,3)} e. {(6,1), (0,3), (4,1), (0,7), (2,5)}

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