Let T:P3→P3 be the linear transformation satisfying T(1)=4x2+7, T(x)=4x+3, T(x2)=−3x2+x−6. Find the image of an arbitrary quadratic polynomial ax2+bx+c.
Let T:P3→P3 be the linear transformation satisfying T(1)=4x2+7, T(x)=4x+3, T(x2)=−3x2+x−6. Find the image of an arbitrary quadratic polynomial ax2+bx+c.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 57E
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Question
Let T:P3→P3 be the linear transformation satisfying
T(1)=4x2+7, T(x)=4x+3, T(x2)=−3x2+x−6.
Find the image of an arbitrary quadratic polynomial ax2+bx+c.
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