p(x) = x³ + x, find [p(x)]B. Problem 3 Let 7 be a linear operator R5 on with minimal polynomial m,(x) = (x² + 1)(x² - 1). Find the rational canonical form for 7.

Q: Show that f(x) = (3x + 2)/(5x-1) is invertible. Determine the domain and range of f and f-1.

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Q: Let f(x) = x + √2x3 + x. Verify whether f[0, 1, 2, 3, 4] = f [0, 1, л, е, -1].

A: The details solution of the given question is given below in step 2.

Q: If ƒ (x) = x − 7 and g(x) = O(-∞, 4) 0 (-∞, 4] O (4,0) O [4,00) O (4,7) U (7, ∞0) what is the domain…

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Q: The set of zeros of f(x) = x³ + 4x² + 4x is (B) {0, -2} (C) {0, 2} (D) {2} (A){-2}

A: find the zeros of the function fx=x3+4x2+4x

Q: The Range of the quadratic function f(x) = -x² + 18x + 52 is O [-9, 00) O [52, 0) O (0,9] O (-∞0,…

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Q: The Range of the quadratic function f(x) = -x² + 9x + 53 is O (0,4] O (-∞,53] O [53, ) O [-53, 4] O…

A: This question is based on finding range of quadratic function which is a downward opening parabola

Q: Find all non-negative integer pairs of (x, y) such that (xy-7)² = x² + y²

A: Find all non-negative integer pairs of (x, y) such that .

Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

Q: 1. What degree are the following polynomials (3.a and 3.b) and monomials (3.c and 3.d)? (a) f(æ) =…

A: Note: According to bartleby we have to answer only first three subparts please upload the question…

Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: Let f(2) = x² +1 and g(z) = z² - 1 Then (fo f)(z) -X (fo g)(x) (go )(x) : x*4-x^2+1 x*4+x^2-1 Note:…

A: Consider the following functions: fx=x2+1gx=x2-1 ffx=x2+12+1=x4+2x2+1+1=x4+2x2+2…

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: Let f(x) = x3 + 5. Explain why f(x) is invertible, then show all steps in the derivation of a…

A: Invertible function and it's inverse.

Q: Suppose we want to form an interpolant at equally spaced points xo = 0, x1 = h, and x2 = 2h of the…

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Q: 10. (a) Describe the transformations of y = x³ into the function f(x) = 8(x-1)³ -5. = (b) Describe…

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Q: ,x2

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Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

Q: For #'s 11 – 14 , h(x) = (ƒ og)(x) Let h(x)= (5x+1)* - (5x +1) and S(x) = x² – x, find g(x) Let h(x)…

A: Given: hx=fgx Q 13: hx=5x+12-5x+1 fx=x2-x Now, As per question hx=fgx=gx2-gx Or gx2-gx=5x+12-5x+1 On…

Q: Let f(x) = 2x + 3 and g(x) = 5æ² + 4x Compute and simplify the following. (f + g)(x) =

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Q: What are the roots of the function f(x) = x³ + x² − 7x -3? O 3, 1+√2, 1-√2 O -3,-1+√2, 1-√2 O 1, 3,…

A: Solution :-

Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

A: First derivative check for monotonicity

Q: Let b be a zero of f(x) = x5 + 2x + 4 Show that none of √2, ∛2, ∜2 belongs to Q(β).

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Q: What is the inverse of the function 2х + 1 f:R → R, f(x) ? 3.

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Q: Consider the function f(x)=√x+5-9 for the domain [-5, ∞0). Find f¹(x), where f -1 is the inverse of…

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