Q 2.8 Consider the functions f₁(x) = x and f₂(x)=3-5cx on the interval of [0,1]. so that a) Find the value of the constant c f₁ and £₂ are orthogonal on [0, 1]. Your answer should be symbolic and should not have any decimals. b) Using the value of the constant c from part(a), find the norm of f2₂ on the interval [0, 1].

Q: 3. Let f(x) = x² + 3 and g(x) = Vx – 3 be functions defined on [0, ∞) and [3, 00), respectively. i.…

A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

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Q: Which of the following is the reciprocal of a linear function? O a) f(x) = b) f(x). = 6 2x + 1 1 x²…

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Q: Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x)

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Q: Be f(x, y) = 1+√16-y². a) Determine and sketch the domain of f; b) Determine the image of f;

A: For a function z=fx, y, the set of real values of x, y for which f(x, y) is defined is called the…

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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: 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: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: A Show that the function f: R² → R defined by f(x₁, x₂) = x² + 2x² + 3x₁x₂ + 4x₁ + 5x₂ + 6 is a…

A: Definition of Vector Quadratic Function : Given Function f: R2→R is a vector quadratic function if…

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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: 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: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

A: We have to write in u(x,y) and v(x,y) form.

Q: h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where…

A: Suppose X and Y are jointly distributed with pdf  where .

Q: (a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB=…

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A: No, we can write it.

Q: 3. Let the function f :R →Rbe defined as follows: [3x–1 if x> 3 f (x)={x² – 2 if -2<x<3 2x+3 ifx<-2…

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Q: Consider z as function of the variables x and y, it is defined by :

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Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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Q: Let F = (2y? + z)i+ 4ryj+ æk. (a) Show whether F is conservative.

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Q: (b) State the range of f for the domain given in part (a). f:A B f(x)=(x-1)²+4. (c) Define the set B…

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