Let be the function f defined on R by { si x < 0 ax? + bx + c si x >0 f(x) = 1. Determine the 3 regions a, b and c such that f is of class C2 C3 ? 2. f thus defined is it of class

Q: 2. Let f be a function defined for all real numbers x -uch that f'(x) < 0 and f"(x) < 0. The table…

A: here we will use relation between a function f(x) and its derivatives to find possible value of W

Q: Let f: R R be defined as f(x) D 1 + x2 Let /= [- 1, 2), then f(1) = Select one: а. 1] b. (0, d. None…

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Q: 1 1r

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Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: 7. Let u be transcendental over F and F< EC F(u). Show that u is algebraic over E.

A: Algebraic field

Q: You are given two functions, f:RR, f(x) = 3x and g:R→ R, g(x) = x + 1 a. Find and record the…

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Q: Use calculus to determine the location and value of the absolute etereme values of f on the given…

A: For maximum or minimum f'(x)=0.

Q: f Gx,y) x+ 3 XY %3D

A: We have to check

Q: If Z- tan () then Show that

A: According to question, z = tan-1yx

Q: 1. Let f be defined on an interval I and let x1 and x2 be numbers on I. If f(x1) < f(x2) whenever x1…

A: Given that: f is deifned in I such that:   f(x1)&lt;f(x2) whenever x1&lt;x2

Q: Determine the range of f, if f: D → R, where f(x) = x². I. D = (-2,2) II. D = [-7,2] III. D = (-4,2]…

A: I. D = (-2,2) Here the variable x lies between -2 and 2, that is,…

Q: Could you write a proof for the following: Suppose F: X → Y is one-to-one. Prove that for all…

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Q: Let 1 f(x) = ,* – 8, – 4 < x < 8 1 The domain of f¯'is the interval [A, B] where A and B = Check…

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Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: Q1. Find the image of the set A= [-2 under function sin x.

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Q: (b) ƒ(AnB) ≤ f(A) Ñ ƒ(B)

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Q: If f is a function from [-2,6] to R, and f(x) = 3x, partition p = {-2,3,4, 6} and tags e = {0, 4,…

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Q: Let X= {p, q, r, s, t}, Y= {1, 2, 3}. how many one-to-one function are there from Y to X.

A: One-One function- A function is said to be one-one if every distinct element from the domain has a…

Q: Consider functions f: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} →→ > {a, b, c, d, e, f}. How many functions…

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Q: Let f: X→ Y and g: Y→ V be functions. Show the following: 3h : Y→X such that ho f = idx (a) f is…

A: Let f:X→Y and g:Y→V be functions, To Prove: (a) f is injective ⇔there exists h:Y→X such that…

Q: 5. Let f be defined by the floor function f(x) = [] and let S = {-3, -2, -1, 0, 1, 2, 3}. a)…

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Q: 13. Let the function f: [a, b] in R be continuous and one-to-one and such that f(a) &lt; f(b). Let c…

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Q: 3. Let f be entire. Suppose that there exist a EC and > 0 such that f(z) & Da, e) for all z E C.…

A: Since f is entire, it is holomorphic on the entire complex plane. Now, we know that f has a root in…

Q: 4. Let f be defined for all real x, and suppose that \fx) – f(v)| < (x – y)? for all x, y e R. Prove…

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Q: If f is differentiable and non-negative on an interval I in R then /3f + 1 is differentiable on I.…

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Q: Let fand g be the functions defined by f(x)= x+et-&x + 1, and g(x) ==- 4x + 2. Let Q and R be the…

A: Hi! All the sub-parts are quite big. As nothing is specified, we are solving (a). kindly re-post the…

Q: and let B = {1,2,3,4}. Provide examples injective surjective injective but not surjective surjective…

A: A function  is said to be injective if , for . That means every distinct element of the domain is…

Q: b) Is f one-to-one? Answer yes or no and explain. Do not just quote the definition, but give a…

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Q: If f is a function from X to Y and A, B are subsets of X then .A f(A – B) = f(A) – f(B) .B f(AUB) =…

A: Given: f:X→Y and a,b⊆X, Find out: To choose the correct option.

Q: 5. Function fand g are defined by formulas as shown below. f(x) = x³ and g(x) = x- 1, for all real…

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Q: c) Is f onto? Answer yes or no and explain. Do not just quote the definition, but give a reason that…

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Q: Let f: A --> B be a function. Show (or disprove) that the following are equivalent. (1) f is…

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Q: If f is an analytic function and does not vanish in a domain D, then prove or disprove the…

A: To Prove/disprove: ∆|f(z)|=|f(z)|-1|f'(z)|2 for all z∈D, where f is a non-vanishing holomorphic…