Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A → C is injective.

True or False A function is a relation between two sets Dand R so that each element x in the first set D is related toexactly one element y in the second set R.

4. (a) (b) Let ƒ : X → Y and g: Y → Z be functions. Prove the following statements. If go f is injective, then f is injective. If go f is surjective, then g is surjective.

Use the mathematical definition of concave and quasi-concave functions to prove that: 3. (a) The sum of two concave functions is also concave. (b) The sum of two quasi concave functions is not necessarily quasi- concave. (c) Quasi-concavity is an ordinal property (a positive transformation of a quasi-concave function is also quasi-concave).

I got stuck on this question. Please explain and answer it clearly please! Thank you!

Let A = {-7, 0, 7} and B = {t, u, v, w}. Define a function F: A → B by the following arrow diagram: F A B и M. (a) What are the domain and co-domain of F? (Enter your answers in set-roster notation.) domain of F = co-domain of F = (b) F(-7) = F(0) = F(7) =

Prove that “if f is decreasing, then f is injective” is true. Show your work.

Let f: A --> B be a function. Show (or disprove) that the following are equivalent. (1) f is surjective (2) f has a right inverse (3) f satisfies right cancellation. It suffices to show three equivalence statements (like a triangle).

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

Discrete Math