Use the functions f and g in C[-1, 1] to find (f, g), ||F||, ||9||, and d(f, g) for the inner product (f, g) = f(x)g(x)dx. f(x) = 1, g(x) = 7x2 - 1 (a) (f, g) (b) ||A| (c) Ilg|| (d) d(f, g)

Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

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Q: Evaluate f (x + y - z)² dV for the box B with dimension: [0, 8] × [0, 7] × [0, 3]. B (Use symbolic…

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Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: 1) Evaluate g = Af, where A and f are given below: (a) (b) (c) (d) A SQRT d³ dr³ + x³ dx 8² 8² +…

A: The step-by-step answer is given below please check.Explanation:Step 1:a) Step 2:b) Step 3:4)…

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: Show that f: R\{2} → R\{5} defined by f(x) = (5x+1)/(x - 2) is bijective.

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Q: Supposer is an invertible function with domain [1, 5] and range [2,7]. Then the domain of r−¹(x − 1)…

A: Given that r is an invertible function with domain [1,5] and range [2,7].It means that for every…

Q: Exercise 5: If f(x) = x5 + 2x³ + 2x, check that f is injective and find (f-1)'(-5).

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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 f (x - y)(y - z) dV for the box B3 with dimension: [4, 9] × [0, 1] × [0, 1]. (Use symbolic…

A: We have to evaluate the integration .

Q: с) V (и-у) - и х(Vху) - ух(Vxи)- (и-V)у+(ү-V)и %3D

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Q: 5x+1 14. Prove that the function f: R \ {2} → R \ {5} defined by f(x) = is bijective. x-2

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Q: For the particular function f(x)=x", me N, show that {} 1 if n = m 0 ifn > m f[xo, X₁, Xn] = ...

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