- Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x − 1. Then the set of functions {f, g, h} is a basis for P2, the set of all polynomial functions of degree less than or equal to two. 2 Express the function A(x) = 16x² - 10x + 8 as a linear combination of these basis functions: A = c₁f + C29 + c3h. C1 , C2 , C3 =

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.CR: Chapter Review
Problem 62E
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Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x − 1. Then the set of functions {f, g, h} is a
basis for P2, the set of all polynomial functions of degree less than or equal to two.
2
Express the function A(x) = 16x² - 10x + 8 as a linear combination of these basis functions:
A = c₁f + C29 + c3h.
C1
,
C2
,
C3 =
Transcribed Image Text:- Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x − 1. Then the set of functions {f, g, h} is a basis for P2, the set of all polynomial functions of degree less than or equal to two. 2 Express the function A(x) = 16x² - 10x + 8 as a linear combination of these basis functions: A = c₁f + C29 + c3h. C1 , C2 , C3 =
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