Use this inner product to find ⟨f,g⟩, ‖f‖, ‖g‖ If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping(f,8) = 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|| forf(x) = 3x² + 4x +7 and g(x) = 2x? – 6x + 4.(f,g)||/| =llg|

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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||

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||

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Use this inner product to find ⟨f,g⟩, ‖f‖, ‖g‖

If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping
(f,8) = 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) = 3x² + 4x +7 and g(x) = 2x? – 6x + 4.
(f,g)
||/| =
llg|

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