For each function below, determine whether or not the function is injective and whether or not the function is surjective. (you do not need to justify your answer). (a) f: r + r given by f(x) = x2 (b) f: n + n given by f(n) = n2 (c) f: zx z → z given by f(n, k) = n +k

First, injective means that for every y, there is only one x such f(x) = y, and surjective means that if f is a function that goes from the set {x} to the set {y}, for every element y in the codomain there is at least one element x in the domain such f(x) = y

(a) f:R----> + R given by f(x) = x2 (i guess you written )

The function is not injective, because f(-2) = f(2), and is surjective, because the codomain is +R, and is always a positive real number.

(b) f:N----> + N given by f(n) = n2  (i guess you written )

As the naturals have no negative numbers, in this case the function is injective, but isn't surjective, because there is no number that when squared is equal to 5, for example.

(c) f: Zx Z → Z given by f(n, k) = n +k:

here the domain is of the form (n,k) and the function is n +k, so the numbers (z,w) and (w,z) return the same value when evaluated in f, then f is not injective. And is easy to see that f is surjective, because in the sum you can reach al the integers on the codomain.

book derives an equation for the volume of a pyramid, as shown in figure 2, and numbers mostly in two settings: for the solutions of polynomial equations, and for 9, we would have to solve the equation for y by subtract- 2. the point (1,. 2) is the center of the circle whose equation is x2 y2. 2x. 4y p.w.c. davies.

step-by-step explanation:

his chances of getting a coin of higher value is 4/19

step-by-step explanation: