f: X → Y and g: Y→ V be bijective functions. Show the following: ) gof: X → V is injective. gof: X→V is surjective. 【 (g° ƒ)−¹ = ƒ−¹ og¯¹

Q: a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain - and range of f(x, y).

A: Solution is given below..

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A: Given,

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Q: Consider the point (x,y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the…

A: We use the distance formula

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Q: Find the analytic function whose imaginary part is v =2xy

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Q: 3) Find the function of y = 1) Reflect about the (2) Shift up (3) Shift X-axis 8 Units left 7units

A: The given function is y=x1) Reflect about x-axis2) shift up 8 units3) shift left 7 units

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A: The function is given by f(x) = 4-x + 2 To evaluate : The graph of the function f(x)

Q: 2. Determine whether these are well-defined functions. Explain. 3 (a) f:R → R, where f(x) = 2² + 5°…

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Q: Given that F′=f, use the substitution method to show that ∫f(ax+b) dx=1aF(ax+b)+C, for nonzero…

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Q: Let P= (x,y) be a point on the graph of y = x. Express the distance, d, from P to (7,0) as a…

A:

Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: Let F = (4xyz + 7 sinx, 2x², 2x²y). Find a function f so that F = Vf, and f(0,0,0) = 0.

A: To find the function f such that F=∇f, we need to find the potential function whose gradient is…

Q: Let u and v be functions of x. Then J (u-v)dx is equal to ux – vx +C dx

A: Topic-:- integration

Q: 8. Let ƒ(x) = = 21/1/2 a) (fog)(x) c) (ƒoƒ)(x) and g(x)= 3x+1, find the following: b) (gof)(x) d)…

A: