1. Define fZZ by f(x) = x² + x + 1 and 9: Z→ Z by g(x) = 2-5x. What is fog? What is go f? 2. Let f AB and 9: BC be functions. Prove that if g of is injective, then f is injective.

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Q: what is this

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Q: Please solve for all steps and show work.

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Q: First, apply the formulas in (9) to find A-1. Then use A-1 to solve the system Ax=b.

A: Here, the given system of equations is Ax=b where,A=[34​23​]b=[56​].It is required to find the…

Q: Don't use chat gpt It Chatgpt means downvote

A: If you have any doubt feel free to ask.

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Solve the following Gourset problem Utt - Uxx Uxx = 0 U|x-t=0 = 4x² U|x+t=0 = 4x.

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Q: Solve the initial value problem xy' -2y=x³ex, y(1) = e.

A: Step 1:Step 2: Step 3: Step 4:

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Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs…

A: Required code:# Visualizing weak convergence in l^2 space # Example: Weakly convergent sequence in…

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Q: Discrete Mathmatics

A: 3.4.

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Q: Find the general solution of the Bernoulli's Differential equation: dy X dx + y = y²x³ cos x

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Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs…

A: Use this code:import matplotlib.pyplot as plt # Setting up a diagram for the tensor product of R^2…

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A: Part 2: Part 3:Conclusion Discussion of the ImageThe image below  illustrates the torus and the…

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Q: What is the answer to this?

A: 6 < 31:The number 6 is much smaller than 31. If you visualize it on a number line, 6 is far to…

Q: Rozwiąż zadanie i podaj odpowiedź

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Q: 2. Are the vectors α1 = a3 (1, 1, 2, 4), (1,-1,-4, 0), linearly independent in R¹? a2 - (2,-1,-5, 2)…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Exercise 3.3.2. Decide which of the following sets are compact. For those that are not compact, show…

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Q: Solve using simplest method and all steps.

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Q: 9. Let f(x) = √√x-2 be a function on real numbers. (a) Find the domain D(f). (b) Find the range…

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