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) = f(x)g(x)dx. f(x) = 3x, g(x) = ex (a) (f,g) (b) ||f|| (c) ||g|| (d) d(f, g)

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

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Q: f(x) = 8+x 8 - x on [4, 6].

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Q: h(x) = (f °gXx) Let h(x)=(2x-5) and f(x) =x, find g(x). 1. Let h(x) = Vx-5 and f(x)= Vx, find g(x)…

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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: 1. Let f(x) = x? – 1 and g(x) = x² +x – 6. (a) Find (f – 9)(x) (b) Find (x) and give its domain. (c)…

A: R is the set of all real numbers

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: f (x) = -x² + 5æ, [0, 5]

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Q: The functions u and w are defined as follows. u (x) = -2x-1 w (x) = 2x²-2 Find the value of u (w…

A: u(w(3))=-33

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Determine the piecewise representation of f(x) below: x) = [9x + 36| Equation A if x2 a f(x) =…

A: we have to find

Q: Define f (x) = Vx² + 1 and g(x) = 2 – x². Find and simplify (go f)(x).

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Q: F(x) = 4 – 3x 1 G(x) x + 1 H(x) = Vx² +5 (a) (F – H)(2) (b) (G • F)(2) (c) (등) (x)

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Q: 1 Let f(x) and g(x) = 4x + 5. - 4 | Then (f o g)(6) (f o g)(x) =

A: The solution is given below :

Q: Let f(x) = 1 and g(x) +4. Then (fo g)(æ) (go f)(x) =

A: (f o g)(x) = x/6 (g o f)(x) =(4x -10)/(x-4)