(a)Suppose that f is an injection. Show that f -1∘f(x) = x for all x∊D(f) and that f∘f -1(y)=y for all y∊R(f).

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Q: Exercise 6.1.10: Find the inverse Laplace transform of 251

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A: As asked we shall use MATLAB to find the roots.MATLAB code is as follows.1f = @(x) 2*x^2 -…

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Q: (c) Prove that there are infinitely many prime numbers.

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Q: 1. Consider the matrices 0 4₁-(13), 1 3)₁ 4₂2 - ( -8 -2) ₁4₁ = (3-2). 0 1 3 -5 -4 A₁-(3) -4 0 and A4…

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A: Two straight lines rotate about two fixed points (-a, 0) and (a, 0) in anticlockwise sense. If they…

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A: Let

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Q: Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine…

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Q: The bar graph below shows the scores that Gabrielle earned on her recent midterm grade report. 100…

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Q: 3. Solve the system of congruences Show the steps used. 3x = 2 7x3 8x 7 mod 7 mod 11 mod 19.

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Q: Find the partition numbers of  f '(x).  (Enter your answers as a comma-separated list.)

A: .

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Q: c Ide Identify the wirten it has a matiman or Maximum point 5 y=x²-9x75 d 2. d) 5 = 3x -x² +9 y = 4…

A: Theorem: Let f: I→ R be such that f has a local extremum (minimum or maximum) at an interior point c…

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Q: Solve the heat equation k a²u 0x² u(x, t) = = u(0, t) = 0, u(L, t) = 0, 0 0 (see (1) in Section…

A: Let u(x,t)=X(x)T(t)From the conditions:u(0,t)=X(0)T(t)=0u(L,t)=X(L)T(t)=0⇒ X(0)=X(L)=0From the…