Let f: XY and g: Y→ V be functions. Show the following: (a) f is injective 3h: Y→ X such that hof= id (b) f is surjective Use: 3h : Y→X such that fo h = v injective if x1 ‡xn → v(x1) = idy ‡ v(xn)

Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

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Q: Find and sketch the domain of the function. f(x, y)=√y+√9-x² - y² y

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Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

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Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

Q: For the function, evaluate the following. f(x, у) %3D 0.7x + 0.4у — 0.04ху (а) f(0, 0) (b) f(1, 0)…

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Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

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Q: Q1 a) let f be a function defined as f(x)=3x² + 2x². Find f(2), f(-1), f(1). b) Define functions f…

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Q: 4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

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