The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3, 2[ e) ]-00, -2JU]5, +0[ f) ]-2, 5[

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: 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…

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 the set A = {x ∈ R | 3x + 2 ≤ 0} has a maximum

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Q: (d) Let ø(x) = x - 1, x > 0. If defines an odd extension of o to the entire real line, then for r…

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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: The equation of a quartic function with zeros -5, 1, and 3 with an order 2 is: * O f(x) = k(x - 3)(x…

A: We have to find the equation of quartic function with zeros -5, 1 and 3 with an order 2. Since,…

Q: Use Fourier-Motzkin elimination to give a linear combination of the following in- equalities that…

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Q: 2. Let f : (0, –→R such that f(x) = x². Show that f(x) < r. • Show that f has no fixed point on (0,…

A: The given function is f:(0,13]→R and defined as f(x)=x2 . we have to show that f has no fixed point…

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

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Q: Prove that f : R – {3} → R – {1}, defined by f(x) = is a bijection. x-1 x-3

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Q: Let f(x) = 3x² and. P = {–2, –1, 0, 1, 2, 3}. Compute Lf(P) and U,(P). %3D %3D

A: Consider: fx=3x2 and P=-2,-1,0,1,2,3. Compute LfP and UfP.   If P is a partition such that…

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: 10.30

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Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

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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: • The domain of f(x) 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, 0) 1 0 2 3 O 4 O

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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: 3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the %3D %3D Intermediate…

A: By rule we solve only first question i.e. Q3 3) Given f(x)=x4-4x2+6g(x)=3x3-8xTo prove the functions…

Q: @show that a) G (x,x) => Uu6) Unl) were G is green funcfion

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Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

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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: Prove that the function : R-{1} →R- {2} defined by 2a f(x)= s bijective. 2 1

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Q: QV2 is Principal Ideal Domain. True False

A: A principal ideal domain is an integral domain in which every proper ideal can be generated by a…

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

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

Q: Define g : (-1, 1) → R by g(x) 1- x2 " Show that |(-1, 1)| = |R| by showing that g is a bijection

A: Concept Used: For a function f:A→B If f is a bijection, then |A|=|B| Consider the function g:(-1,…

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: 3. For f (x) = 2x³ + 4x² + 3x – 7, prove that there exist a number k such that f(k) = 20.

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Q: Show that the mapping f:R2 → R² defined by f(x1, x2) 5x2) is linear. = (2x1 + x2, -3x1 +

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Q: Prove that ax² bx C + + (x − a) (x −b) (x −c) (x-b) (x-c) x-c -+1 x³ 3 (x-a)(x-b)(x-c)

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Q: Show that  ℝ2 = span([1 1], [1 -1])

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Q: 7. Find the minimum of, f(x1, x2) = 2x? – X1X2 + 2x³ + x³ – 2x1x3 And check the second order…

A: This is a problem of multi-variable calculus.

Q: Prove directly that the functions f1(x) = 1, f2(x) = x, and f3(x) = x² = x² are linearly independent…

A: 27. The given functions are f1x=1, f2x=x and f3x=x2. For this we have to show that…

Q: QV2] is Principal Ideal Domain. True False

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Q: prove V injective if x1 ‡xn → v(x1) = v(xn)

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Q: Let x y, z be three non-negative integers such that x + y + z The maximum possible value of xyz + xy…

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Q: Let fi = 1+2x + 2x² + 3x³, f2 = 2+3x + 3x² + 4x³, f3 = 3+ 5x + 5æ² + 6x³ and 9i =1+x+x², g2 = 1+x…

A: Given polynomials are; f1=1+2x+2x2+3x3,f2=2+3x+3x2+4x3,f3=3+5x+5x2+6x3…

Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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

A: Ix=2x-18 Now let, y=2x-18 Now to find inverse function interchange x and y, then solve for y in…

Q: Let  g(x) = x2−2x−4 on [-2, 4] , then the fixed points for g(x) are

A: A fixed point in a function is following below situation. f(x) = x. Similarly in above case. g(x) =…

Q: 1 If f(x, y, z)= of then x- y- 3z ду а. 1 (х— у-3-)* b. -1 | (х-у-3-)? С. (х — у-3-)? d. 1 (х-у-3-)2

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Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: 4) Show that and are eventually fixed points for the function : 8 4x Osx< 2- 4x sx< f(x) = - 1 4x –…

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Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: Prove that f(x) = x2 + 2x is not injective.

A: The function is said to be injective if f(x)=f(y) it implies x=y

Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

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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: 7. Find the minimum of, f(x1, x2) = 2xỉ - x1x2 + 2x3 + x3 – 2x1x3 And check the second order…

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