Suppose that f: X → Y and let AC X and BCY. a counterexample: counterexample: a (a) Prove or give (b) Prove or give (c) Prove or give a counterexample: (d) Prove or give a counterexample: ƒ−¹(ƒ(A)) ≤ A B ≤ ƒ(ƒ−¹(B)) f(AUf-¹(B)) = f(A) U B. ƒ−¹(ƒ(A)^B) = An ƒ−¹(B)

Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyexz k, - C: r(t) = (t² + 1)i + (t² − 1)j +…

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Q: Find the linear approximation L(x of the function f(x) =V1– at a = 0. L(x)=mx+b where m is - and b…

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Q: The domain of the function h(t) = vt – 9 is O [9, 00) O R O (-00,9) O (9, 00) O (-∞0,9]|

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Q: The domain of the function f defined by e5x+3y+9xy5 f(x, y)= √130-5x²-5y² is equal to: In D = {(x,…

A: We are given the function all for two variable for which we need to verify if the given set is…

Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: Compute [ f(x,y) dA, where f(x,y) = y²√ and D is the set of (x, y) such that x>0, y> x², and y<10-…

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Q: Let f: X→Y be a function, and let A,BCY. Prove or disprove: f-¹(A)uf-¹(B).

A: The given statement : f-1(A ∪ B) = f-1(A) ∪ f-1(B) is true and we shall prove this statement.

Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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Q: a) f(AUB) = f(A) U ƒ(B). b) (i) f(An B) ≤ f(A)n ƒ(B). (ii) Find a function f {1,2} → {a}, and A, B C…

A: a)  We  have  to prove  that  Now,      Thus,  (Proved)[since, b) i) We  have  to show  that Let  be…

Q: f(x,y) = x²y + 2xy² + 5y³

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Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

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Q: (x – c)2 + 160 Let the function p be defined as p(x) = where c is a constant. If p (c) = 10, what is…

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Q: z) = (x2 + then (a + E

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Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

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Q: Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n…

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Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

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Q: Let f:Rx R→ Rx R be given by f(a,b) = (3a + 2b,2a –b) a, b) ERx R. 1) Find f(2,3) and f(– 1,4). 2)…

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Q: Consider F and C below. F(x, y, z) = yzexZi + eײj + xyeײk, C: r(t) = (t² + 2)i + (t² − 1)j + (t² −…

A: In the given question we have to evaluate : a) The function f(x, y, z) .  b) Evaluate the integral.

Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

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Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: For fx) = Vx and g(x) = x + 4, find b. the domain of fo g a. (fo g)(x) (f o g)(x) a. (Simplify your…

A: Given that two functions:

Q: Consider teu tunction: fcx) = -x+2x +4 Calculate f(x +h) for any constant h f(x +h) - f(x)

A: The given function is fx=-x3+2x+4. (a) Evaluate f(x + h) as  follows.…

Q: 2. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): z² (a) f(z)=z³+z+1;…

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Q: Find the domain of the function f(x, y, z) = √√ xyz². O A. Domain = {(x, y, z) ER³ : xy ≥ 0} O B.…

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Q: Iff: X→Y is an injective function and A, BCX then: f(A-B) f(A)- f(B)

A: Use the concept of injection map of functions.

Q: 04 Let f(x) be a contineous function such that Ler - 5/W)dx = = 4 and =9, then a) 81 b) 101

A: Use definite integration property

Q: Find all functions f:R → R that satisfy the equality xf(y) + yf (x) = (x+ y)f(x)f(y) %3D for all r,…

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