f: R → R. be a function given by f(x₁,x2,...,xn) = x².x..., where = 1. Show that the maximum of f(x1, x2,...,xn) is n¹/.

Q: Let f : R R:f(x) = 10x + 7. Find the function g : R→R such that gof = fog = IR. %3D %3D

A: Given f: R -> R  such that f(x) = 10x + 7 and  g : R -> R such that g o f = f o g = IR

Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

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Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

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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: Find the domain and b) Sketch the domain of f(x, y)= In(4x² – y) -5 -2 -1 3 4 5 x

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Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

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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: Describe the domain of the function f(x, y)= In(6+x-y). {(x, y): y<x-6} {(x, y): y 2 0} a. {(x, y):…

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Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: Exercise 4. Let F and G be homothetic functions in two variables. Is their sum homothetic? [Hint,…

A: We will use the fact that the MRS of a homothetic function is always homogeneous of degree 0. Let…

Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

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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: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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Q: Consider the function ƒ (x, y, z) = 2x² + 5y² + z². a) If ƒ (x, y, z) is the profit made from…

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Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: Show that the following relations are not functions on R. a) ƒ = {(x, y) = RxR | y=x/(x² −7x+12)}

A: Given function. y=xx2-7x+12 is not define for x2-7x+12=0 =&gt; (x-3)(x-4)=0

Q: осод ва меньва оз 4.th order. вида у со.в), comest Фу decimal placesi 16 - д-х2, у (06) =117379

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

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

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Q: f :R →R, f(x) = 3 + ax² + bx +11 fonksiyonu (-3,5) aralığında 20 - azalan ise atb-kaçtır ? If the…

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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: Seven office mates, three women (Fran, Gladys and Helen) and four men (John, Karl, Leonard and…

A: iv. KarlExplanation:From the given restrictions, let's find who will be absent: Fran will definitely…

Q: Find the range of the function f : R R,f(x) = x² – 4x + 3. Select one: a. [-1, c0) b. (-∞, 1] U [3,…

A: The objective is to find the range of the function.

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: A = [a,b), be an (right half-open) interval of R. 6 (c) (d) a,be R+,b+00, Explain whether f(A) is…

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Q: Let f(2) = z2 + 2|2|2 + z where f is differentiable. Determine the set of all points zo where f is…

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Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

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Q: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

A: f: R2 → R, f(x1, x2) = x1-x2 function is given. a) Can f be an surjective function? b) Can f be an…

Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: 2. Let us define a. Verify that f(x, y) = c. Now consider the function git Similarly, consider the…

A: Given Data: Let us consider the given function is fx,y=xyx2-y2x2+y2

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

Q: Evaluate the Riemann integral f'(x) dx by using definition with the tion = {₁,"+11/ n Pn= i=1 n+1…

A: Given Data: Let the function f:R→R be defined by fx=-1x2x≠0,0x=0To evaluate the Riemann integral…

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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Q: 3. Let f A B be a function, and let Ao C A, BoC B. Prove that (a) f(f(f(Ao))) = f(Ao); (b)…

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Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…