D: Remind that the set F of all functions from R to R is a vector space. 2. Prove that for any function f the function e(x) is odd. What is their sum? = f(x) + f(-x) 2 is even and the function o(x) = = f(x)-f(-x)

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

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Q: Give the domain of the function. Зх — 2 - z = O {(x, y): x and y are real and y + 3x - 2} - {(x, y):…

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Q: evaluate the functions for the specified values, if possible. f(x) = x² + 10 g(x) = = Vx - 1 %3D 22.…

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Q: What're the residues of the function z/(z + 1)? а. 0.25i and 0.75i b. -0.25 and -0.75 С. others d.…

A: The given problem is to find the residues of the given complex function.

Q: x + 1 (b) Let f(x) = and g(x) = x²+1. x + 2' ii. Determine if f and g are one to one or onto. iii.…

A: According to question given that f(x)=x+1x+2, g(x)=x2+1

Q: Let v1 =[1,4,-2] , v2 =[-2,-3,7] , b =[4,1,h] FIND all value(s) h such that b is in span{v1 , v2 }

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Q: Let 5 —7: х x E хе [3, -2] —4. х —1 х€ (-2, 0) хE (-0, 3) f(x) = 7. х — 3 1 хе(-2, о) Calculate…

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Q: Let A = {1,2,3}, Define the functions f: A → C and g: B → C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) =…

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Q: Q21) One of the following is correct for functions the f(x)=1,g(x)= x³ and h(x) = ln(x): a) f(x),…

A: To check the linear independence we shall find the Wronskian for the given three functions. To find…

Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

Q: Which of the following four functions is (are) linear functions? Function A: y=x - 2 Function B: ソ=…

A: Explanation of the answer is as follows

Q: g(x) さリ-x+5 In Exercises 21-38, evaluate the functions for the specified values, if possible. f(x) =…

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Q: of Əf Find and дх ду Əf дх — II for the following function. f(x,y) = (5x – 2y)5

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Q: 1.) Given the function f(x,y)= 2+y=x² find and sketch the domain of f.

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Q: What is the domain of the function f (x) : (-1,0) U [1, 00) b. (-1,0] U (1, ∞) c. (-00, –1) U [0,1)…

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: Show that the function f : R→ R : f(x) = x° is one-one and onto.

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Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: The domain of the function g(t) = /t – 9 i. O (-0, –9) O R-{9} O (9,00) O [9, 0) O R

A: all the values which can be used as input in a function is called domain of a function

Q: Let X = { n Î Z | 1 £ n £6 } and consider the two functions f : X ® X , g : X ® X , expressed in…

A:

Q: (c) For a polynomial p = a + a₁x + a₂x² + + anx", let p denote the polynomial obtained from p by…

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Q: Use the Second Shift Theorem to determine i. F(3te-(t+5)²) F-1 e3(w+2)j ii. 3+(w-5)j

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Q: Which of the following is the domain of the function g(x) 2-x 0(-00,2 O (-00, 0) O [0, ∞0) O (-0, 2)

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Q: Let R denote the set of real numbers. Let f: Rx R-> Rx R be a bijective function defined by f(x, y)…

A: Introduction :

Q: — 2х1 — 5х2 + 8хз x1+3x2 – 5x3 +x4 |3x1 + 11х2 — 19хз + 7x4 X +7x2 — 13хз + 5х4 x1 X2 . Let T X3 X4…

A: The given transformation T can be written as            Tx1x2x3x4=-2-58013-51311-19717-135x1x2x3x4is…

Q: Find f, and fy, and evaluate each at the given point. f(x, y) ху (2, –2) X - y ,(X, v) = ,(x, v) =…

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Q: A TUN f: {1,2,3,4} is defined by f(1) = 6, ƒ(2) = 7, f(3) = 8, Drag the answers into the right place…

A: Given function is f:1, 2, 3, 4 → 5, 6, 7, 8 defined by f(1) = 6, f(2) = 7, f(3) = 8, f(4) = 6