3. If f:(X,r)(Y.A) and g:(Y,A)→(Z,r) are open functions, prove that gof :(x.r)(Z.r) is open function.

Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

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Q: Prove that there does not exist any function f(x, y) such that

A: To show that there does not exist any function that satisfies the given conditions

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

Q: 3. Let f(x) = x² + 3 and g(x) = Vx – 3 be functions defined on [0, ∞) and [3, 00), respectively. i.…

A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

Q: 4. If f:(X,r)(Y.A) and g:(Y.A) (Z,r)are closed functions, prove that g of :(X.r)(Z.r) is closed…

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Q: f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X→V is injective. ) gof: X→ V…

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Q: f: X→Y and g: Y→V be bijective functions. Show the following: ) gof: X→ V is injective. ) gof: X → V…

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Q: Which of the following is the reciprocal of a linear function? O a) f(x) = b) f(x). = 6 2x + 1 1 x²…

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Q: Let f e E(0, ox) and let a be a positive real number. Define the function fa as follows Sal) = {";…

A: Properties of Laplace transformation

Q: Suppose UCC is a domain, f, g = O(U). If |ƒ(z)|2 + |g(z)|² = 1 for all ZEU, show that ƒ and g are…

A: The solution to the problem is in the segment below.Explanation:To show that f(z) and g(z) are…

Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

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Q: The coordinates of vector x = (3, -2, 4) relative to basis B = { (0, -3, 4) , (1, 0, 0) , (O, 4, 3)…

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Q: Let f(x) = (x + 1)² - 1, x 2-1. Then the set {x:f(x) = f(x)} is

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Q: Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R,…

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

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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

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Q: Supposer is an invertible function with domain [1, 5] and range [2,7]. Then the domain of r−¹(x − 1)…

A: Given that r is an invertible function with domain [1,5] and range [2,7].It means that for every…

Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

A: We are given that B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3). We need to show that g is…

Q: Show that f(x) = e describes a bijective function from R to (0,+x). (a) Show that f is a function.…

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Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

Q: {h,p,t, v, w}, and 7, 10, 12, 15, 16, 21, 24, 29, 30}. 21), (р, 29), (t, 24), (v, 24), (w, 10)} de n…

A: We have to complete the given statement according to the given information

Q: Let the function f: R R be defined by f(r) = 3r -5. Prove that the function is bijective.

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Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A: Given that  where G,u and v are differentialblle functions

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

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Q: b) Let f: D→ C be a function and Y a subset of C. Show that f¹ [C-Y] =D-f¹ [Y].

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Q: 2. Let us define a. Verify that f(x, y) = af ду xy(x² - y²) x² + y² af y(x² - y² + 4x²y²) əx (x² +…

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: 6. Let f(x) = x55x+1. Prove that f has at least 3 zeros in [-2, 2]; that is, there exist distinct…

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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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: Let f : A → B be a function. Prove that if C C A and D C A and f is injective, then f(C) = 7 (D) =→…

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Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.