4. Define the operators T and U on the space P(R) of all polynomials in variable x as follows: T(f(x)) = f'(x), U(f(x)) = f(c). Is the relation TU = UT valid? Find the operator TU – UT.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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4. Define the operators T and U on the space P(R) of all polynomials in variable x as
follows:
T(ƒ(x)) = f'(x), U(f(x)) = xƒ(x).
Is the relation TU = UT valid? Find the operator TU - UT.
Transcribed Image Text:4. Define the operators T and U on the space P(R) of all polynomials in variable x as follows: T(ƒ(x)) = f'(x), U(f(x)) = xƒ(x). Is the relation TU = UT valid? Find the operator TU - UT.
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