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(x)g(x)dx. = f(x) = 1, g(x) = 9x2 - 1 (a) (f, g) (b) (c) ||g| (d) d(f, g)

Q: Suppose f(x) =1 - 3x and g(x)= √x+5. a.) Show that f(-1)= g(11). b.) Find x such that f(x)= g(4)

A: (a) To show: That f-1=g11. Given: The functions are fx=1-3x and gx=x+5. Calculation: Substitute x=-1…

Q: Show that f(x) = (3x + 2)/(5x-1) is invertible. Determine the domain and range of f and f-1.

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Q: Evaluate the commutators of the operators (a) d/dx and 1/x, (b)d/dx and x2.

A: Given:  a)  ddx and 1x b) ddxand x2 To Find: Commutator of the operators

Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

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Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini The number of…

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Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

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Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: given that f(x) =x-1, and g(x) =2x2 -1, determine (g (dot product) f)(x)     i put "(dot…

A: The given function is: f(x)=x-1           and             g(x)=2x2-1

Q: Use the functions f and g in C[-1, 1] to find (f, g), ||F||, ||9||, and d(f, g) for the inner…

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Q: Calculate R5 for f(x)=4x2+6x over [-1,1]

A: The objective of this question is to calculate the Riemann sum, specifically R5, for the function…

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

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Q: Find the domain of the square root function: w(x) = Vx + 25 x > 25 (-0, –25] [-25, о0) (-0, –5) U…

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Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

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: Specify the symmetry of the following functions: (a) y (x1, x2) = 4(x1 – x2)² + T0 xf+x3 (b) p(x1,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: D = {[x, f(x)]: (-1, 2), (0, 1), (1, 2), (2, 5), (3, 10)} Write the rule for f(x). x + 1 2x x² + 1

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Q: 3. Find the Domain of the function : h(x)= x²-5 (a) (-00, -5] U,500) (b) R (c) (-0,5) (d) (-5,5]

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Q: Find f (x) and simplify ) /(x) =5'+3r'+4e-2c b) a)%3(r'+3r+2r(2x a) c) /(x)=(4x-2r+ 7)

A: (a) Consider the given function fx=5+3x4+4ex-2ex-lnx7