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: Use the linear approximation (1 + x)k s1+ kx, as specified. 13) Find an approximation for the…

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Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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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: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

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Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

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Q: 5. Express the given function using unit step function: * [t f (t) = 0st<4 2 , t24 O A.) f (t) = t…

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Q: Definition: Let f : D → Y be a bijection. The inverse function f-1 : Y → D is a function such that…

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Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

A: We have to fund the value of gv(u=-1,v=1).

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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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: f(xo+h, yo+h) = f(xo, yo) + [fx (xo, yo)h + fy(xo, yo)k] 1 + xo, Yo)h² +2fxy(xo, Yo)hk + fyy(xo,…

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Q: Consider the function h : Z xZ → Z× Z defined by h(x, у) 3D (2ху, 7x — Зу). (a) Is h injective? (b)…

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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: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: Let f(x) =|x²-2x|, the ceiling function, and let S be the interval S =(1,3). Then f(S) is one of the…

A: fx=x2-2x S=(1, 3) fs=f1=12-21=1-2=-1 fs=f3=32-23=9-6=3   Given f(x) is a ceiling function  According…

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: Find fax, fay and fry for the function f(x, y) = (1+x+y)e¯xy Select one: a. None of these b. fxx –…

A: Consider the given function : f(x,y)=(1+x+y)e-xy

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

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. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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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: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

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: Consider F and C below. F(x, y, z) = yzexi + e*²j+xyek, C: r(t) = (t² + 1)i + (t² − 2)j + (t² − 3t)…

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