If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-3)g(-3) + f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, g), ||f ||, ||g|| for f(x) = 3x + 4x +7 and g(x) = 2x? – 6x + 4. (f,g) = || || = llg||

Q: Describe the transformations for f(x) = 4log[- 3(x − 2)] + 1 from its base function.

A: The function .To Find:Describe the transformation of the given function.

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: inverse

A:

Q: has a invers

A: If f has a inverse

Q: y = -3(5)-2-1 1

A: Complete details of transformation applied is explained stepwise in the picture attached below.

Q: Use Lagrange interpolating polynomials of order 4 to calculate (7.1) 1 3 8 Ax) 1 20 94 267

A:

Q: product of irreducible polynomials.

A:

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: 2. Describe the transformations that map the base function y = 2* , onto the - 3(2**) - 3 given…

A: We will describe the transformation.

Q: True or False: One major assumption for conjoint analysis is that products are bundles of…

A: In this case, we need to identify the given statement is true or not.

Q: Expand the following function in terms of Legendre polynomial: 35(cos(theta))^4

A: Given the function,                           35cos4θ.

Q: injective/surjective/bijective? f(n) = n^2, g(n) = n + 3, h(n) = { n + 1 if n is odd…

A:

Q: Suppose that g and h are inverse functions, and that g(–50) = 25, evaluate h(25)

A: It is given that g and h are inverse functions and- g-50=25

Q: Show that if a function has a unique right inverse, then it is necessarily bijective.

A: When the composition of two functions is the identity function, the functions are referred to as the…

Q: - Let f(x) = 3* a) What is f(x) ? c) Use the table from b) to complete the table for the inverse…

A:

Q: Under what conditions (if any) are polynomials (over R) injective? Surjective? Bijective? Explain…

A: Let us consider the n degree polynomial px=anxn+an−1xn−1+......+a1x+a0. Here, an≠0 and x∈R…