Exercise 2.20 Find the Fenchel conjugate for each of the following functions on R: (i) f(x) = ex. { (ii) f(x) = -In(x) 8 x > 0, x ≤ 0. (iii) f(x) = ax² + bx + c, where a > 0. where IB =[-1 11.

Q: he absolute extrema of J(*) = ,2+2x +9 n(-1,5]. %3D

A: The given function is  f(x)=xx2+2x+9 on [-1,5]

Q: Q1. Let f(x) = V2-x,g(x)=/5+x, then find the following : (1) (F-g)(- 1) (ii) (iii) domain of…

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Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: 9: Check Euler's Theorem for the Function

A: We checked Euler's theorem for function.

Q: (-x if x < -2 4. Let f(x)=x² if-2<x<2 Compute the following function values: (0 if x ≥ 2 a) f(-3) b)…

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Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: A1). Sketch the graph of ONE function such that ALL of the following hold: i). f"(x) 0 for x> 2…

A: Graph of function

Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

Q: 5. Lif f(x) = x3 + ax? + bx + c, determine the values of a, b, and c if f(x) switches from concave…

A: Given: f(x)=x3+ax2+bx+c Differentiate the function. f'(x)=ddxx3+ax2+bx+c=3x2+2ax+b Differentiate…

Q: 1.) Given the function f(x,y)= 2+y=x² find and sketch the domain of f.

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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 スeso and its oder for the function f(z) = 1-x +Z + ě. %3D

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Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

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Q: Find a function f(1) such that | f(z)dr= 2² – 5.

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Q: Find the standard factorization of the entire function f(z) = cosyz

A: Using the Euler's formula as, cosθ+isinθ=eiθcosθ-isinθ=e-iθ Now adding both the equations,…

Q: Determine where the function f(x) = O A. (-∞, ∞) 1-00 O B. O C. O D. 3 3 3 (-∞0,²21) U ( 212,00) N/W…

A: we have to find out the values of x where function is continuous.

Q: Write the formulas of fog for pairs of real functions f, g. (a) f(r) = x², 9(x) = x – 2 (b) f(x) =1,…

A: A composite function is generally a function that is written inside another function. Composition…

Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

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: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…

Q: List the transformations that are applied to f(x) = Vx to produce f(x) =-2(x+3) -4

A: Vertical transformation: Vertical translating the graph is shifting the graph up or down in the…