1- Which of the following is a homomorphism? a)O f:Z→Z, f(x) = x+2 %3D b) O f: Z12 → Z30, ƒ(x) = 20x %3D 0of: Z5 → Z30, f(x) = 6x %3D d) f:R - R, f(x) = x²

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: Small changes in numbers in an integrand can result in very different methods required for…

A: We evaluate the integral by using different choices for b.

Q: Let T: P2 → P2 be defined by T(p(x)) = xp'() A. Describe the kernel of T. B. Describe the range of…

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Q: Let f: Z/4Z → Z/2Zx Z/2Z be defined by f([0])= ([0], [0]), ƒ([1]) = ([1],[1]), f([2]) = ([0], [1]),…

A: We see,         [2] = [1] + [1]    but, f([2]) = ([0], [1])          f([1]) + f([1]) = ([1], [1]) +…

Q: Which transformation includes a reflection off (x) = (x – 1)² + 1 over the y-axis? Of'(x) = (-4x –…

A: Given query is to find expression which has reflection over y axis.

Q: 8. State the transformations applied to y = f(x). a) y = -3f(x) b) y = f(2x) – 7 c) y = f(-x) d) y =…

A: Given function  y=f(x)

Q: 4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and…

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Q: 2. Prove that ƒ : (R × R, +) → (R, +) given by f(x, y) = x + y is a homomorphism. Is g : (R × R, +)…

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Q: 2. Let : RR and y: R+ → R be mappings with 6(x) -2e-x. (a) Find the range of y. = 1. Use your answer…

A: Here's a summary of the answers:  Solutions:(a) Find the range of γ (b) Use the definition to show…

Q: 6. Let S = {-1,0, 2, 4, 7}. Find f(S) (image of S under f) where f is from R to R for (a) f(a) = 1…

A: The

Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

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Q: 4) Let ƒz = dƒ/əz and ƒz = 0ƒ/əz. Recall ƒ = u + iv, the notation f is used for the complex…

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Q: 1 The mapping (x, y)(x+h, ay + k) can transform 1 y= f(x) into y +2 +7f((x+3)). What would be the…

A: Kindly do rate this  helpful.Thank You

Q: 6. Where are the following functions di: x+2 a) f(x) = %3D V(x+2)x

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Q: Let A = {1,2,3}, let S = P(A) and let RC S x S be a relation defined by the rule (X,Y) E R…

A: Given .Let  and  be a relation defined by the following rule..

Q: 3. Describe the map T* if T = L(C³) is defined by T(x1, x2, x3) = (0,x1, x2).

A: Sure, so let's break it down. The map (T∗) here is a transformation that takes a point…

Q: 5. Describe the transformations that map the base function y = 5* onto y = 5-2x-4 + 1 HINT: y =…

A: Given base function y =5x  and transform function  y=5-2x-4+ 1