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: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

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Q: 5. (a) Let f: S T be a function, and A CT and BCT be subsets. Show that (A-B) = f-1(A) - f-(B). ww

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Q: Let f be the function given by f(x) = Jax + b for x 2 where a and b are constants

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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: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: find functions f and g so that f ∘ g = H.

A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: IfY C X, show that inf (X) < inf (Y)

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Q: The domain of the function f(x,y)= V1-x²-y² +In(x²+y² – 1) is empty Select one: O True O False

A: we have to find the domain for f(x)

Q: Differentiate the function f(t) = yt (a + bt).

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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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: 1. f (x, y) = x² + y?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: z) = (x2 + then (a + E

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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: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

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

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Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

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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