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: Show that the function f(x) = 2x³ – 1, from f: R → R is bijective and find its inverse.

A: The function f(x)=2x3-1, from f:ℝ→ℝ

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

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Q: Use proof by contradiction approach to prove that VxM) V N(X)

A: This is a problem of Predicate Logic.

Q: (Q. +,.) is a subfield of (F = {a + bV5: a, b e Q}, +,.); (F = {a + bv5: a, b e Q}, +,.) is a…

A: A non-empty subset F' of a field F is a subfield of F if F' is closed with respect to the…

Q: Show that f:Z-->Z ; f(x)=x+2 is invertible

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Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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

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Q: b) Determine whether the given function is a bijection from R to R. f(x) = (x+ 65)/(2x + 65)

A: Let us consider a mapping f: A→B then the function is said to be bijective  f is one one  function…

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: 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: Let f(x) = (x + 1)² - 1, x 2-1. Then the set {x:f(x) = f(x)} is

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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: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

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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: Consider f = {(x, y) : x ∈ N and x + y = 5}. Write out some elements of f. What are the domain and…

A: Given: f={(x,y): x∈N and x+y=5} The domain of a function f(x) is the set of all values for which the…

Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

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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: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, |lg||, and d(f, g) for the inner…

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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: Z is the set of integers, R is the set of real numbers. 4) Find the inverse of functions a) f:…

A: (a) Consider the function, f:[0,∞)→[0,∞) defined by fx=x2+12 For x∈[0,∞), fx∈12,∞. That is, range…

Q: Show that f(x) = e describes a bijective function from R to (0,+x). (a) Show that f is a function.…

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Q: 10) What is the domain of f(x)= vx + 5? A) {x|x 2 -5} B) {x|x 2 0} C) {x\x> -5} D) {x|xs -5}

A: Domain is set of collection of x for which f is defined

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

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

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Q: Use the functions f and g in C[-1, 1] to find (f, g), f, g, and d(f, g) for the inner product (f, g)…

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Q: What are the roots of the function f(x) = x³ + x² − 7x -3? O 3, 1+√2, 1-√2 O -3,-1+√2, 1-√2 O 1, 3,…

A: Solution :-

Q: Gue Functions fandg, FindCa) Cf g) C&) and its dlomiain, and b) (g oF (x) and its. O F(x)--6xtq,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, ||g||, and d(f, g) for the inner…

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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: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

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