Find an example of a function ƒ: N → Z which is (a) injective but not surjective (b) neither injective nor surjective

A function g : Z → Z is defined as g(n) = |n| + 1. Show that this function is not injective and not surjective.

In each part of this question, you are asked to give an example of something, and show that it is an example. (a) A bijective function f : Z→ N. (b) A surjective function R→ Q.

Let's consider all the functions f : {1, 2, . . . , n} → {1, 2, 3, 4}, n ≥ 5. How many of them are: a) injective functions b) increasing functions c) non-decreasing functions d) surjective functions?

A function that is [Select] interval [a, b] has [Select] on a [Select] on that interval.

Consider the function f : Z × Z → Z × Z defined by f(a, b) = (a + b, a − b). Is f injective? Is f surjective? Justify your answers.

Let f be a function from Z×Z to Z×Z (that is, f maps pairs of integers to pairs of integers) given by f (x, y) = (x + y, xy). Is f one-to-one? onto? Prove or give a counterexample

Proficiency #16. [Compositions of Functions] Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are functions such that gof is onto, then f is onto.

Let n be a positive integer and let f : [0..n] → [0..n] be an injective function. Define the function g : [0..n] → Z as g(x) = n - (f(x))². Prove that is also injective.

Discrete Math