Let f: X→ Y and g: Y→ V be functions. Show the following: (a) fis injective 3h: Y→ X such that ho f = idx (b) f is surjective 3h : Y→ X such that fo h = idy =

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: Find div F for F(x. y, 2) = (xy, 5 - zy, x +y). Select the correct answer below: O x- O y-? O x-5- O…

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Q: S (x, y)= I+x* + y? 1-x² - y? 2. Determine the points at which the function is continuous.

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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: 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 fff f(x, y, z) dV for the specified function f and B: SSSB f(x, y, z) dv = f(x, y, z) = 2/…

A: We need to evaluate: ∫∫∫Sf(x, y. z) dV where f(x, y. z)= zx and2≤x≤6, 0≤y≤8, 0≤z≤8 This can be…

Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

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 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: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

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: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r – s, s - 3r). Use the table of…

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Q: me please: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let

A: We have given that X1, X2 ∼ Unif(0, 1)

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: 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: 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: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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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: 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: Consider the function f(r, y) = 212 + ry – 6ry + 5x +2. (a) Show that (1,3) is a stationary point of…

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Q: Iff: X→Y is an injective function and A, BCX then: f(A-B) f(A)- f(B)

A: Use the concept of injection map of functions.

Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

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Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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Q: dA XB d(AXB) = Ax dB mp np %3D np Prove that where A and B are differentiable functions of u

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