Let ƒ: R → R and g: R → R be of the form f(x) = ax + b and g(x) = cx + d where a, b, c and d are constants. Determine necessary and sufficient conditions on the constants a, b, c and d so that fog=gof

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A: Linear Transformation :If U and V are two vector spaces, over a field F. Then the mapping T:U->V…

Q: Let A = {1, 2, 3) and let f : A A, defined by f = (1, 2), (2, 3), (3, 1)}. Find f, if it exists. %3D

A: given A = {1, 2, 3} this is function

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A: f:ℝ2→ℝ and g: ℝ2→ℝ f is C2 Hf4,5=2-1-13 g is defined by gx,y=fx-y,yx

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

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A: Explanation of the answer is as follows

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Q: of Əf Find and дх ду Əf дх — II for the following function. f(x,y) = (5x – 2y)5

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Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

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A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

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Q: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

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Q: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

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Q: (a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB=…

A: Let x1,x2,....,xn+1∈ℝn We take n=5. then x1,x2,x3,x4,x5,x6,x7∈ℝn There exists two sets A and B,…

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