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12. Consider the continuous function y = f(x), such that ƒ(x) is not a piecewise continuous function, and f(x) = f(-x) except for x = 0, on the interval [-a, a]. If [_ª* f(x)dx = 2 [ª f(x)dx What can we say about f(x)? A) f(x) must be an even function. B) f(x) must be a odd function. C) f(x) must be an odd and even function.

12. Consider the continuous function y = f(x), such that ƒ(x) is not a piecewise continuous function, and f(x) = f(-x) except for x = 0, on the interval [-a, a]. If [_ª* f(x)dx = 2 [ª f(x)dx What can we say about f(x)? A) f(x) must be an even function. B) f(x) must be a odd function. C) f(x) must be an odd and even function.

Advanced Engineering Mathematics
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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12. Consider the continuous function y = f(x), such that f(x) is not a piecewise continuous function, and f(x) = f(-x) except for x = = 0, on the interval [-a, a]. If [_^* 1(x) dx = 2 * f(x) dx 0 What can we say about f(x)? A) f(x) must be an even function. B) f(x) must be a odd function. C) f(x) must be an odd and even function. D) There is no such function. E) None of the above.
Transcribed Image Text:12. Consider the continuous function y = f(x), such that f(x) is not a piecewise continuous function, and f(x) = f(-x) except for x = = 0, on the interval [-a, a]. If [_^* 1(x) dx = 2 * f(x) dx 0 What can we say about f(x)? A) f(x) must be an even function. B) f(x) must be a odd function. C) f(x) must be an odd and even function. D) There is no such function. E) None of the above.
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