Problem 1. Compute (showing a complete derivation) the Fenchel conjugates of the following functions. 1. f: R R, with f(x) = e. 2. 4-1,0 (the indicator function of the interval [-1,0). 3. Ha} (the indicator function of the singleton {a}).

Q: Given the graph of f" (x) at what values is there a possible inflection point? y 2 4 8 O 1, 4, and 7…

A: We have to check

Q: 18. The graph of the function f shown in the figure to the right has a vertical tangent at the point…

A: A graph of the function is given.The aim is to find the points in the interval  for which  is not…

Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

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Q: 1. Calculate the subdifferential of the following functions. It might be helpful to draw the…

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Q: 9. Given the functions /(x) = 2x + 5 and g(x) = x? – 4, find (4) x. b. C. d. 2x-5

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

Q: Which graph shows the function f(x) = 3 sec (2x) +1? RIN 14 12 10 8 00 6 4 2 -4 -6 -8 -10 -12 2 B 2…

A: Given f(x) =3sec(2x)+1 We have to choose the graph of this f ,from given option below.

Q: 4. Consider the following graphs and compute the given compositions. y = f(x) y = g(x) 3 -3 -1- -3…

A: We know,  (f∘g)(x)=f{g(x)}

Q: a. Graph f(x) = In x and (x – 1)?, (x – 1) (x – 1)* on the viewing window [-2, 4, 1] by [-5, g(x) =…

A: Consider the equations:

Q: Apply the tranformations indicated for the graph of the general functions given | g(x) (-1,-4) х /2…

A: Note: Points are not labelled correctly in the given graph, I have corrected them. Solution: All the…

Q: 1.4 Given f(2) = (z + 5i)g(2). If is it also know that g(-5i) = 0, then which of the following…

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Q: 7. Create an equation for f(2), a cublc function that has z-intercepts given by the set {-2,-3, 1}…

A: The function is given to be cubic, hence it will be of degree 3. The general form of this function…

Q: 1. Write the domain of the following functions and draw a corresponding picture. f(x, y) = In(y-x)…

A: To find the domain of the function  f(x,y)=y−x2ln(y−x)​, we need to identify the values of ( x ) and…

Q: z+1 (a) (z2-16)(z+2)

A: We have to identify the poles first.

Q: Use the graph of the function f shown to the right to find f(-3), f(- 2), and f(- 1). 10 f(-3)= ts…

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Q: Q.2: Find the interval in which the function is (a). Increasing, (b). Decreasing, (c). Concave Up,…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 5. Given f(x) = -2/4x – 8 +1 a. Determine the parent function b. Determine the mapping rule c. Map…

A: Given function

Q: Sketch a graph of the function f(x) = -2/2 7 654 3 2 1 -1 - z2 - 3 cos(x) - 2 37/2 2x 57/2 3 7x2

A: The given function can be graphed as below.

Q: Enter all answers in the answer blank separated by commas. (1)- 3-3i 3+ 3i + 22 (2) z2 +1 3z -1 (3)…

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Q: 2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 1 – 2n? and g(n) = 3n + 2. %3D (a)…

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Q: (iv) p(39), where p is the Euler p-function.

A: Euler totient function and residue classes

Q: 1.4 Given f(2) = (2 + 5i)"g(2). If is it also know that g(-5i) = 0, then which of the following…

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