Problem 1.3. For each function fi, determine whether it is injective but not surjective, surjective but...
Prove If the functions are injective, surjective, or bijective. You must prove your answer. For example, if you decide a function is only injective, you must prove that it is injective and prove that it is not surjective and that it is not bijective. Similarly, if you claim a function is only surjective, you must prove it is surjective and then prove it is not injective and not bijective. - Define the function g: N>0 → N>0 U {0} such that g(x) = floor(x/2). You may use the fact that...
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: R Codomain: R f(x) = x3 O Injective O Bijective O None O Surjective
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: R Codomain: (-1,1] f() = sin(x) O Surjective Bijective O None Injective
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: A= = {1,2,3,4,5,6} Codomain: B = {u, V, W, X, y, z} f = {(3,w), (4,2), (1,y), (6,w), (5x), (2,u)} O Bijective O Surjective Injective O None
Problem 5. Determine whether each of the following function is injective and/or surjective. (a) f : R → R, f (r) = 2x – 1 (b) f : Z+ Z, f (r) = 2x – 1
Discrete Math The following functions all have domain {1,2,3,4,5} and codomain 1,2,3. For each, determine whether it is jective, bijective, 3. (only) injective, (only) sur neither injective nor surjective. or 1 2 4 5 3 (a) f 1 2 1 2 1 2 3 45 1 (b) f 1 2 1 2 3 if x 3 (c) f(x) if x >3 x -3
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) = x² – 3, f2(x) = x2 – 2x and f3(x) = x. Show that B is a basis of P2. (b) Determine whether or not the following sets are subspaces of F. (i) X = {f € F | f(x) = a(x + cos x), a € R}. (ii) Y = {f EF | f(x) = ax + sin x, a € R}. (c)...
Click here to watch the video. Consider the function f(x) = 2x2 - 4x-1. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum opmaximum value and determine where it occurs. c. Identify the function's domain and its range. a. The function has a value > > Click to select your answer(s) and then click Check Answer. 3 parts Clear All remaining 20 F3 FI F2 - F4 75 $ 2...
Warm-Up: Subgradients & More (15 pts) 1. Recall that a function f:R" + R is convex if for all 2, Y ER" and le (0,1), \f (2) + (1 - 1)f(y) = f(2x + (1 - 1)y). Using this definition, show that (a) f(3) = wfi (2) is a convex function for x ER" whenever fi: R → R is a convex function and w > 0 (b) f(x) = f1(x) + f2(2) is a convex function for x ER"...
Can someone please check to see if I am doing this right? Please write legibly if you post revisions in comments, thank you! (5) Let A {q, r, s, t and B = {17, 18, 19, 20}. Determine which of the following are functions. Explain why or why not. а. fSAX В, where f — 1. q, 17), (r, 18), (s, 19), (s, 20) Answer: this is a function because in function 'f element 's' is related to 1 element...