what is an odd function If you let f x 1 x f x 1 x then f f is a symmetrical odd function its graph is in quadrants I and III but f 0 f 0 is undefined So you can say f 0 f 0 is either 0 0 or undefined Or if you want to stick to terminology about graphs the graph of f f either passes through the origin or it does not intersect the y y axis at all
1 An odd function is a function where f x f x If you graph an odd function you will find that the graph has rotational symmetry around the point 0 0 Also worth noting is that odd functions are made up of polynomials where x is raised to an odd power Share Cite answered Sep 19 2013 at 15 43 I have the standard definition of an odd function from wikipedia Again let f x be a real valued function of a real variable Then f is odd if the following equation holds for all x and x in the domain of f x f x
what is an odd function
what is an odd function
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That is the proof We used the fact the f 0 was odd i e f 0 f 0 We then note that 0 0 so we can write f 0 as f 0 We then have that f 0 f 0 We conclude that f 0 0 dave If you are asking how to prove that f 0 f 0 let a f 0 and so a f 0 a a 2a 0 a 0 1 An odd degree mononomial is an odd function A polynomial is an odd function if every one of its trms is of odd degree Thus x17 5ox9 35x x 17 5 o x 9 35 x is an odd function But the degree of a polynomial is defined to be the degree of the term of highest degree the so called leading term so 3x3 5x2 3 x 3 5 x 2
The idea of the proof you presented is that 1 f x can be rewritten in the following way f x f x 2 f x 2 f x 2 f x 2 This follows by just cancelling terms on the RHS 2 Show that the first term is an even function and the second term is an odd function Let g x f x 2 f x 2 Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers
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We know from elementary calculus that the integral of an odd function on L L vanishes When f is even then f x cos px is even and f x sin px is odd It follows that the imaginary part of Fourier transform vanishes Consequently F p is real When f is odd then f x cos px is odd and f x sin px is even Hence the function is an odd function Share Cite Follow answered Aug 15 2017 at 16 31 Sarvesh
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