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Problem 5. Determine whether each of the following function is injective and/or surjective. (a) f :...
Problem 1.3. For each function fi, determine whether it is injective but not surjective, surjective but not injective, bijective, or neither injective nor surjective. Explain why. (1) f1: R20 + R with f1(x) = x2 for all x ER>, where R20 = {x ER|X>0} = [0, ). (2) f2: R20 + R20 with f2(x) = x2 for all c ER>0. (3) f3: R + Ryo with f3(2) = x4 for all x € R. (4) f4: R R with f4(:1)...
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: 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
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
Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective). And Find a left inverse for f or explain why none exists.Find a right inverse for f or explain why none exists. (a)f:Z−→Z, f(n) =n2. (d)f:R−→R, f(x) = 3x+ 1. (e)f:Z−→Z, f(x) = 3x+ 1. (g)f:Z−→Zdefined byf(x) = x^2 if x is even and (x −1)/2 if x is odd.
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...
Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explain why. (b) Determine if f is surjective. Explain why Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explain why. (b) Determine if f is surjective. Explain why
2. Show that the function f:N→Q defined by f(n) = is injective but not surjective.
(1) For each of the following functions, determine if it is injective and determine if it is surjective. Justify your answer. (a) f : R → R, f(x) = 2x + 3. (b) g : R → R 2 , g(x) = (2x, 3x −1). (c) h : R 2 → R, h((x, y)) = x + y + 1. (d) j : {1, 2, 3} → {4, 5, 6}, j(1) = 5, j(2) = 4, j(3) = 6. (2)...
8. Prove the following: a. A function, f: X Y, is injective if and only if If-2013 1 for each y EY b. A function, f:X + Y, is surjective if and only if \f-1(y) 2 1 for each y E Y c. A function, f:X → Y, is bijective if and only if \f-(y)= 1 for each y E Y