Let f(x) = ax + b and g(x) = bx +a, where a and b are integers. If f(1) = 6 and f(g(19))-g(f(19)) = 10, find the product of a .... The product of a and b is

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Q: Let m & n be constants and suppose f(x) = {" + 3bx + 2x² , x 1' тx + b What are the values of m and…

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Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

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A:

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A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: Given that f(x)=x^(2)+3x-70f(x)=x2+3x-70 and g(x)=x+10g(x)=x+10, find f(x)/(d)iv g(x)f(x)-:g(x) and…

A: Answer

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A: Find derivative and sum of coefficient.

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Q: Analyze the polynomial function f(x) =x-(x- 2) using parts (a) through (e).

A: Please find attachment for the details solution

Q: Let f(x) = x³ + x + 4 and g(x) = 3x + 2 in Zs[x]. Then, upon dividing %3D f(x) by g(x), we get None…

A: f(x)=x3+x+4 and g(x)=3x+2 in Z5[x].

Q: find the interverse of the fuction f (x)= 2x + 3/x-4

A:

Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

Q: How does the linear factorization of f(x), that is, AX)=an (x-c1)(x-c2) (x-C). show that a…

A: Here the linear factorization of the function f(x) is given as:…

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −3

A: Let us find a polynomial with a degree of 2 and a zero x=-3 A factored polynomial with a zero -3 has…

Q: Let f(x) = x' + 2x + 4 and g(x) - 3x + 2 in Z,[x]. Then, upon dividing f(x) by glx), we get 7- The…

A: I am solving part7 &amp; part8 as you mentioned.

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Q: Find the derivative of the function?

A:

Q: Let f(x) = x3+ x +4 and g(x) = 2x + 3 in Z3[x]. Then, upon dividing f(x) by g(x), we get The…

A:

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

A:

Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: Show that ax2 + 2bx + c dx | (Ax² + 2Bx + C)² will be a rational function of x if and only if one or…

A: The given integral is ∫ax2+2bx+c(Ax2+2Bx+C)2dx Let us assume that the integral is a rational…

Q: Show that if the quadratic polynomial f (x) = x2 + rx + s takes on both positive and negative…

A: Find the real roots of the polynomial,

Q: Find the quadratic polynomial g(x) = ax2 + bx + c which best fits the function f(x) = 2x at x = 0,…

A: To find the quadratic polynomial gx=ax2+bx+c which best fits the function fx=2x at x=0, in the sense…

Q: Let k(x)=f(x)g(x)h(x). If f(x)=3x−2,g(x)=2x−3, and h(x)=−2x2+4x, what is k′(1)?

A:

Q: Express the polynomial x3 + 2x + 3 EZŞ[x]as a product of irreducible polynomials of Z5[x].

A: Explanation of the answer is as follows

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: Given that f(x) = 3x²- 3cx +2, find c such that if f(x) is divided by (3x – 1), the remainder will…

A: Using synthetic division we have to find the value of 'c' for which the following function when…

Q: If f(x)=/2x and g(x)=1-x², then (gof)'(x)= %3D

A: =&gt;(g.f)(x)=g(f(x))

Q: 2. Use the Intermediate Value Theorem to show thatf has a zero between a and b: f(x) =x+2 x*- 6…

A:

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

A:

Q: Find the maximum of f (x) = 4x – 1.8x² + 1.2x3 – 0.3x* using Quadratic interpolation (xo = 1.75, x,…

A: We can solve this using quadratic interpolation formula

Q: 1. Use the Intermediate Value Theorem to show f(x)= 2x +6x² – 3 has a zero between a = -3 and b =…

A: I am attaching image so that you understand each and every step.

Q: f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x²

A:

Q: 10. For f(x) = 2x3 + 7x + 4, g(x) = 4x? + 4x + 6, and h(x) = 6x² + 3 in Zg find f(x) + g(x)h(x) with…

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Q: For j(z) = (3x2 - 7) (-2x* + 7x), find j' (x) by applying the product rule. Provide your answer…

A: j(x)=(3x2-7)(-2x3+7x) The product rule is: (fg)'=f'g+fg' From above:  f(x)=3x2-7g(x)=-2x3+7x Now,…

Q: If g (x) = 3x² + 12x – 96 on the interval [-8, 4]: What value of C satisfies Rolle's theorem?

A: here we have to use the result of the Rolle's theorem.

Q: Find a third-degree polynomial p(x) that is tangent to the line y = 14x − 13 at the point (1, 1),…

A: Let px=ax3+bx2+cx+d   →1 be the required third-degree polynomial. Differentiating with respect to x,…

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ E R. -

A: Given, x.f(x-1)=x-3.f(x),  ∀x∈R put x=0 in equation 0×f(-1)=-3f(0)f(0)=0 put x=1…

Q: If f(x) = ax + bx + c has zeros x = 15 and x = 6, what zeros does f(x + 1) have?

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Q: Find gof. f(x) =x², g(x)=x- 4 († +zx) O

A: Find gof

Q: Given that f(x) = x² + 12x + 35 and g(x) = x + 7, find (f · g)(x) and express the result in standard…

A: Given : f(x) = x2+12x+35 g(x) = x +7

Q: there is at most one polynomial of degree less than or equal to n_____ option,(a) which interpolated…

A: Using interpolation theory, We need to check which option is correct.

Q: 9. For the polynomial function f(x)= x³ - bx² + cx-24 where b,cel, all of the following are…

A: The given function is a cubic polynomial: f(x)=x3-bx2+cx-24     , here b,c∈I If p is a zero of that…

Q: For f(x) = 2x + 1 and g(x) = x² – 7, find (f- g)(x). %3D O A. 2x2 - 15 O B. -x² + 2x- 6 O C. - 2x -…

A: Given that : The functions , f(x) = 2x + 1  and g(x) = x2 - 7 .