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

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A: Use Hessian matrix

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Q: Find the domain of the function. Then compute the value of the function at the given point. f(x,…

A: To calculate domain of f(x,y)

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

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Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

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Q: Definition: Let f : D → Y be a bijection. The inverse function f-1 : Y → D is a function such that…

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Q: 4. Consider the function Check whether f is concave, convex or neither. f(x, y) = x² - y² + 2xy + 2x…

A: Please find attachment for the details solution

Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: Derive the autocorrelation function of: x₁ = $xt-1 + εt + 0€t-1 assuming that p < 1, and E(?) = 0²,…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

A: We have to fund the value of gv(u=-1,v=1).

Q: Given a function f: A → B and subsets X,Y C B, prove that f"(XNY) = f(X)nf-(Y).

A: He we will prove the given result.

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: Consider f(x) = 3|x|, which is in R[-2, 2]. %3D b. Use the function F(x) to find ſ², f.

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Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

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: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Let f(x) =|x²-2x|, the ceiling function, and let S be the interval S =(1,3). Then f(S) is one of the…

A: fx=x2-2x S=(1, 3) fs=f1=12-21=1-2=-1 fs=f3=32-23=9-6=3   Given f(x) is a ceiling function  According…

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Let Y be a function of the RV X as follows: YA SX, x², x Compute fy (y) in terms of fx (x). Assume…

A: Given that fX(x)=12πe-12x2   If Y=X, then  fY(y)=12πe-12y2         =12πe-12x2

Q: Let F(x, y) =. Evaluate (31) F dr (1,0,0) O a. 9 + 3e3 8+ 3e3 С. 8— Зе3 O d. 10 – 3e3

A: We will use basic knowledge of vector calculus and integral calculus to answer this question.

Q: Determine if the following functions are analytic or not: 1. f(z) = (z* + 1)³ – 3z* where z is the…

A: (i) The  given function is ;               fz = z*+13 - 3z* We know that a function  f is analytic…

Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

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Q: Consider the function: 3.3 x²+yⓇ 0 if (x, y) = (0,0) if (x, y) = (0,0) a - Determine if f is…

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Q: of the apples is equal to 3 of the oranges. If there are 12 mor 5 In a fruit stall, - - annles than…

A: Fraction:  A small part of something.  In other words, numerical value that is not a whole number A…