Given the functions f and g where f: R → R, f(x) = x – 3 and g : R → R, g(x) = 2x a) Find f + g. b) Find fg. c) Find fo g. d) Is fog invertible? If ves, find the inverse function.

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A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

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A: Determine the radius

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A: Change the z in the terms of u and v and the differentiate.

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Q: (-1+i/3)°, by using deMoivre 's theorem

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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A: Complex integration of the function

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: Let z = g(x, y) = f(3 cos(xy), y + e#y) provided that f(3,7) = 4, f1(3,7) = 2, f2(3, 7) = 3. i) Find…

A: Here option(g) is true because

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

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Q: Q/ z = x + f(a) and a = ry. Show that: 尝-端=

A: We use the definition of partial derivatives to prove the given result.

Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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