If possible make an explicit bijection from [0, 1] to [-2, -∞. If no possible, Why? If f(x)=(5x+1)/(x-2) is bijective, show this to be true by function f :R — {2} →R— {5}

Q: find all Zeras of the tunction f(x)=1ax²-13x²+/ enter the Leras seperated by commas.

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Q: Show that the IVP x" = -6x(x')3, x(-1) = -1, x'(-1) = 1/3, has a unique solution x and find the…

A: Consider the given equation. x''=-6xx'3 And the initial values are x-1=-1 and x'-1=13. Let the…

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A: To determine the maximum range of values of x for which the given initial value problem has a unique…

Q: ¤1 + ag – r3 = 0, -2r1 – 12 + 5r3 = 0, -#1 + 4.x3 = 0 find the Rank(A), where 1 1. -1 A = -2 -1 -1…

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Q: Show that the function f: R - {2} (arrow) f: R - {5} defined by f(x) = (5x+1)/(x-2) is a bijection.

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Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: Find the monic quadratic polynomial, q(x), such that •1

A: Given:

Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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Q: Prove that the function f:Q Q given byf(x) = 2x – 3 for all x E Q is bijection

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Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of f-1

A: fx=2x-18 Now consider, fx1=fx2,                   where x1, x2∈ℝ⇒2x1-18=2x2-18⇒2x1=2x2⇒x1=x2…

Q: ALL for f*) Such tatt FIND FUNC TIONS Vx - x² +1 :(^),f

A: The given derivative of a function f(x) isf'(x)=x-x2+1x

Q: a) Use Backward difference to find the Finite difference equation of the follow ди ди o'u -= C- xe…

A: We are given the equation ∂u∂t+a∂u∂x=c∂u2∂x2 , x∈ 0 , 1  , t≥0 Let us consider a grid of points in…

Q: 6 2, find the following. - V (gof)(x) 2√2(1-2x) X (b) the domain of (gof)(x) in interval notation −…

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Q: 7. Suppose f(x) = x³ – 27x + 1. Prove that f has exactly one root (zero) in the interval [0, 2].

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Q: 7. Find the absolute maximum and absolt f(z) = 2x – 31²/3 on the interval -1,2). %3D

A: We have to find out maximum and minimum

Q: Find the point that mdximizes the f(xg)= x?+y?- 6x +9 funciion depercling on the g(x,y)=y-x²=0…

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Q: 7. Verify that the function f(x) =x3-x'-6x+2 satisfies the hypotheses of Rolle's Theorem on the…

A: Given:Verify that the following function satisfies the hypotheses of Rolle's Theorem on the interval…

Q: Find the linearization at x = a. f(x) = 1 a = 5 x3 (Express numbers in exact form. Use symbolic…

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Q: The functions f, (x) = 3x2 – 1 and f2(x) = 5x³ – 3x are orthogonal on the interval [-1,1] True/False…

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Q: A natural cubic spline S for a function f is defined by +3 x² x 3 + 3 2 1≤x≤2 2≤x≤: 3≤x≤ 5(x) = - 12…

A: Given, A natural cubic spline ,s for a function.…

Q: - R-{-}→R-{} defined by f(x) = Show that f: R 3x-5 2x+1 is bijective.

A: Given function is f: ℝ - -12 → ℝ--32 such that f(x) = 3x-52x+1

Q: Show that the function f(x)=3x-2 is a bijection.

A: For a function is to be bijective, then the function should be well defined, surjective, and…

Q: Find the exact intersection points of the functions: f(x) = 2cos2x +5sin x- 11 g(x) = 8sin2x – 6sin…

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Q: Find the linearization at x = a. f(x) = 9x*, a = 1 %3D (Use symbolic notation and fractions where…

A: We have to find the linearization of the given function.

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: @ f(x)= x²-3x-4 2 @ f(x) = x² - 4x +3 Show that whether f(x) reduceable Poly or not

A: The given problem is solved below in detail.

Q: 1 2. Consider the function defined by f(x) = over [-1, 1]. SET-UP the Lagrange %3D 1+ 12x²…

A: Given function is fx=11+12x2 over interval -1, 1. Now 11 equally spaced nodes on -1, 1 are -1, -0.8,…

Q: find the absolute maxima and minima of the func-tions on the given domains. ƒ(x, y) = x2 + y2 on the…

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Q: Q1) check the continuity of fX) at X- -1, 0,1.23 -1<x<1 2x-1, 3x-2 25x53 2, x=3

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Q: Test for symmetry: 6x2 +5y* = 2 m soolaisvic tni-y d niomoc Ans 11a Determine whether f is even,…

A: 11.a The given equation is, 6x2+5y4=2. Test for symmetry: An equation is symmetric about x-axis, if…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

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Q: If g(y) is differentiable for 2 < y < 3 and g(2) = g(3) = –-1, then there is some 2<a< 3 such that…

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Q: show that g(x) = (1/2)x has a unique fixed on [0,1]

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Q: Please see attached equation image as I didn't want to enter it incorrectly in this text box

A: Given function is h(x) = f(g(x)) where The function h(x) is given by:

Q: Show that the IVP x" = –6x(x')3, x(-1) = -1, x'(-1) = 1/3, has a unique solution x and find the…

A: The given initial value problem is, x''=-6x(x')3                                     ..............1…

Q: 10. If f(x) = x³ – 3x +1 is defined on [0,1], then by using False position method, find the first…

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Q: 4) Consider the function fex)= Slx-s] Evaluate 7-4 for any There is no solution to the equati on…

A: Given: fx=5x-5 so, f7-f47-4=57-5-54-57-4=52-13=513=53

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Q3. Prove that if g interpolates the function f at ro, T1, . .. , In-1 and if h interpolates f at…

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Q: 10. Find all of the discontinuities that exist for g(x) = 2*+3x-4 Show any work required to %3D x+1…

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Q: Q1(i) Prove that Lim + a+ 1 2n²+1 V2n²+2 V2n²+n]

A: (1) Given, g(x)=limn→∞12n2+1+12n2+2+.....+12n2+n suppose any f(x) and g(x)…

Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

Q: [-x, 7] aralığı üzerinde f(x) = cos x fonksiyonunu ele alınız. f(x) için 0 and x2 = T (düğüm)…

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Q: on the closed interval Co,14], (0,14)such that f'ccF FC14D-FCO) 14-0

A: we have to find the value of c

Q: If f(x)=x^3/3 -3x Show that f(x) satisfies the hypothesis of the Roll's Theorem on the interval [-3,…

A: Topic:- rolls theorem

Q: Find the linearization L(x) of f(x) at x = a. f(x) = 3square root of x, a = 27 show all work

A: fx=3x, a=27 Differentiating with respect to x, we get f/x=3·12x    ∵dxdx=12x=32x Now,…

Q: Find the linearization at x = a. f(x) = a = 7 (Express numbers in exact form. Usc symbolic notation…

A: Linearization L(x) of the function f(x) at x=a can be written as below: L(x)=f(a)+f'(a)(x-a)

Q: 3 Q7- Let fw=ex-y, Find a fun ction y =gcW So that f. 9) (x) = X+ 2 .

A: Given f(x)=2x3-4 To find a function y = g(x) such that  (fog)(x)=x+2