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: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A: We know that, Total profit = Total revenue - Total cost

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A: Composite functions

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Q: Show that x – P VB + (d - x)* g(x) is a decreasing function of x.

A:

Q: 2 nd the domain of the function f(x) : (x² – x – 12)(x2 + 1)

A:

Q: The interpolating polynomial p(x) of degree 2 of f(x) = 6xª – 2x³ + x² + 9 is p(x) = x² + 9. %3D…

A:

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: (d) Compute P(x 2 2).

A: Given that  X~Poisson(μ=6) Probability mass function of X is  f(x)=μxe-μ/x!  , x=0,1,2,3,____

Q: Pls help

A:

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: If P(x) = x +x+ 4, find P(7). P(7) =

A:

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: f(x+h)-f(x) for f(x) = 2x2 +11 : Find %3D

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Q: -1 Let g(x) = 8x + 16 and f(x) = = ax + b. If g(x) = 2f(x) find 8ab.

A:

Q: Find f(k-1) when f(x) = 5x² + 4x + Of(k-1) = 5k² - 6k + 10 f(k-1) = 5k² - 6k + 2 f(k-1) = -6k² + 5k…

A: Introduction: A polynomial function is a function that involves only non-negative integer powers or…

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: f(x)=x(40-x)/(20+9cos(x)) Let the function and the set V=[10,15,20,25,30]. Consider the set W of…

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

A:

Q: Determine Number of Zeroes Num of the Polynomial function: F(x)=x²₁²-9x Zero (5)

A: We have to find zeros