Let f: X → Y and g: Y → V be functions. Show the following: (a) f is injective 3h : Y→ X such that ho f = id, (b) f is surjective 3h: Y→X such that fo h = idy Use: v injective if x1 xn → v(x1) ‡ v(xn) # How to prove these Ihs) Can you explain id x How to proof with the arrows (do you prove both rhs and

Q: Let In, f be real fun ction on 52.Show {w : fu(w) yo frw) }=Ŭ o U {w-1fu(w) %3D f(w)1>と3

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A: We have to do implicit differentiation.

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A: We have to check

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Q: oints, where the function f ఐ,00)

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

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Q: Let z be a differentiable function of x and y related by the equation: x z ++* =(√√y+cosh(z))". X 2…

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Q: 1 is IR? \ {(0,0)}. 22 + y2 The domain of the function f(*, y) True O False

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Q: Consider the function f with domain (-o, o0) whose second derivative is given 20x(r +3) (22 – 1)3 a)…

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Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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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: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

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Q: Let z be a differentiable function of z and y related by the following equation: 1+1=(√y+cosh(z)) ².…

A: Given: The equaiton is x+zx-z=y+coshz32. To find: The value of ∂z∂y at the point 3,0,0.

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Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

A: we have to evaluate the following by using greens theorem

Q: Suppose f: X→ Y, and A, B CY. Prove that (a) f¹(AUB) = f¹(A) U f¹(B).

A: Union of two sets A and B is denoted as A∪B  It contains all the elements that are either in A or in…

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Q: Differentiate the given function y = cosh(In(6x*)). 1 а) О Зг? + 4 x4 1 b) O 92? 4 x4 c) O 3z2 1 3x²…

A: Given function is y=cosh(ln6x3)

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A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: 3. Let f be a bounded continuous function on C and a E C. Show that f(z) dz lim 0. iz]=r (z – a)²…

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