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||

Consider the function: g(z) = with the domain IR\{8} (i.e. all real numbers except 8) and the image R\{1} (i.e. all real numbers I+10 except 1). Find the expression for the inverse function g(r). Select one: O not in the list O (10+8x)/(x-1) O 10+8x O (10+8x)/(x+1) O (x-8)/(x+10)

Calculate the following commutators: (a) [O₂, O6]; (b) [O₁, O₂]. The procedure is to calculate [A, B] by expressing A(B) - B(A) in the form C.