If f(x) and g(x) are arbitrary polynomials of degree at most 1, then the mapping (f,g) = f(-2)g(-2) + f(2)g(2) defines an inner product in P2. Use this inner product to find (f, g), ||f||, ||g||, and the angle af between f(x) and g(x) for f(x) = 5x +7 and g(x) = -5x. (f,g) = ||f|| = ||g|| = radional

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 4E
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If f(x) and g(x) are arbitrary polynomials of degree at most 1, then the mapping
(f,g) = f(-2)g(-2) + f(2)g(2)
defines an inner product in P2. Use this inner product to find (f, g), ||f||, |lg||, and the angle af,g between f(x) and g(x) for
f(x) = 5x + 7 and g(x) = -5x.
(f,g) =
||f||=|
||g|| =
afg=
r
(radians).
Transcribed Image Text:If f(x) and g(x) are arbitrary polynomials of degree at most 1, then the mapping (f,g) = f(-2)g(-2) + f(2)g(2) defines an inner product in P2. Use this inner product to find (f, g), ||f||, |lg||, and the angle af,g between f(x) and g(x) for f(x) = 5x + 7 and g(x) = -5x. (f,g) = ||f||=| ||g|| = afg= r (radians).
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