Use the functions f and g in C[-1, 1] to find (f, g), ||f||, |lg||, and d(f, g) for the inner product = [+ f(x)g(x)dx. (f. g) = f(x) = 5x, g(x) = ex (a) (f. g) (b) ||f|| (c) ||g|| (d) d(f, g)

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

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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: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 3x + 1. 1 h(x) = V3x + 1 f(x) =D

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Q: Let f(x)=√(x+1/x),g(x)=2/√(x-1) and h(x)=x^2+1 Describe the domains of f(x) and g(x) . Find…

A: We have to find domain

Q: Differentiate. y =x° In x- dy II

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

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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: ,x2

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Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

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Q: g(x)= f (x)-(f(x))" +(f (x))* for all xeR. Prove that f (x) and g(x) increase or decrease together.

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Q: Let ƒ(x) = (2x + 3)(3x2). Use the product rule to find ƒ′(x).

A: Consider the formula for product rule. Product rule: fg'=f'⋅g+f⋅g'

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: Consider the quadratic function V(x)= ax +bx + cx +2x,x, -4x,x, -2x,x,, try to find the range of…

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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: Suppose f(x) = Evaluate: f(x) dx (A - In (2) (B) 4 3 16 (D) In (2)

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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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