Define \( T: P_2 \to \mathbb{R}^2 \) by \[ T(p) = \begin{bmatrix} p(4) \\ p(6) \end{bmatrix}. \] Find a non-trivial element of the kernel. \[ p(t) = \underline{\hspace{3cm}} \]

Q: Consider the points (x₁, y₁) (-1,6), (x2, 12) (0, -2), (x3, 13) (1,4), (X4, Y4) = (2,4). + = x + =…

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) = 4 - 8x. h(x) = (4 – 8x)³ – 7(4 – 8x)² +…

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Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Firstly make the divided difference table x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl Pxi ,…

Q: The domain D, of the function f (x) = Vx² – 1 is: -

A: The domain of a function is set of values for which the function is defined. The square root is…

Q: 3 3 Let AÄx) = (10x – 15) + 9 and g(x) = (16 – 8x) – 7. Find all values of x for which g(x) < f(x).

A: Given: fx=3510x-15+9 gx=3816-8x-7 When, gx≤fx…

Q: The function f is given below. Find f1(x). 2x-4 f(z) = %3D x-5

A: to find an inverse function, interchange variables, and solve for y

Q: Discuss the cases of Gaussian elimination method. • Determine the domain: 10 4 f(x) =- x3 – 64 Write…

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Q: Let f(x) = 2x2 - 1 and g(x)= 1 + x². Find (f o f)(x). O x* +2x² +2 4 O 4x4 – 4x2 + 2 | 4 O 2x* + 4x²…

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Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

A: The objective is to find the value of 2c3-c2

Q: Pls help

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Q: (4) Given f(x) = x³ – 6x² – x +6. a) (2 pts) Use the leading term to determine the end behavior of…

A: The end behavior of a polynomial f(x) is the behavior of the graph of f(x) as x approaches to +∞ or…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Newton's Divided Difference table is given by x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl…

Q: B. Find the domain of 1. h(x) = (x – 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1 and g(x) : x + 3 -1 3. If…

A: Domain is the set of all possible values of x (independent variable) for the function.

Q: Find the zero of P(x)=7x-12

A: We have to find the zero of P(x)=7x-12.

Q: Let f(x) = 2x + 8, g(x) h(x) — 3х — 6. = x + 2x – 8,and Perform the indicated operation. (Simplify…

A: Given that fx=2x+8,gx=x2+2x-8 and hx=3x-6To find :f-gxSolution :f-gx=fx-gx=2x+8-x2+2x-8…

Q: Given the function C(t) = – 10(t – 4)°(t + 5)°(t – 7) a. List the zeros (separated by commas) b.…

A: we have to find zeros

Q: Find the zeros of the following functions and determine their multiplicities: (a) (2 – 1)3; (b)…

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Q: Find the local maxima and minima of f (x) = x - 3x2 24x +5 a. X1 = o(MAXIMA), X2 = 3 (MINIMA) O b.…

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Q: 2x + 5 Find all the asymtptotes of f(x) : x – 1

A: We need to find asymptotes.

Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x) =/x +1. h(x) = (\/x + 1)*

A: NOTE: Refresh your page if you can't see any equations. .

Q: For the polynomials p(x)=4x* – 3x² +x -1 and d(x) =x² – 1, write in the form p(x)= d(x)q(x)+r(x).

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Q: Given the function P(x) = (x – 2)(x + 5)(8x – 4), find its y-intercept is its x-intercepts are x1 =…

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Q: Given the function C(x) = (x – 3)( – 9x + 5)*(x – 7)°, its roots are and their multiplicities are

A: Given, C(x)=(x-3)(-9x+5)4(x-7)9

Q: find all polynomials P(x) and Q(x) satisfying, for all x∈R the equalities: P(Q(x))=x4-5x2+7 and…

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