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3. Let A be the set of all functions ƒ : 0, 1] → R that are continuous in the interval [0, 1]. Recall that I : A → R defined as I(f) = | f(x)dx is a function. (a) Prove that I is surjective. (b) Show that I is not injective.

3. Let A be the set of all functions ƒ : 0, 1] → R that are continuous in the interval [0, 1]. Recall that I : A → R defined as I(f) = | f(x)dx is a function. (a) Prove that I is surjective. (b) Show that I is not injective.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Let A be the set of all functions f: [0, 1] →R that are continuous in the interval [0, 1]. Recall that I : A → R defined as I(f) = | f(x)dx is a function. (a) Prove that I is surjective. (b) Show that I is not injective.
Transcribed Image Text:3. Let A be the set of all functions f: [0, 1] →R that are continuous in the interval [0, 1]. Recall that I : A → R defined as I(f) = | f(x)dx is a function. (a) Prove that I is surjective. (b) Show that I is not injective.
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