Dear Student, Please find below the solution to the asked query: A function is odd function if f-x=-fxafx=x4-2x2⇒f-x=-x4-2-x2=x4-2x2=fx⇒f-x≠-fxHence fx=x4-2x2 is not odd function bfx=x-x2⇒f-x=-x--x2=-x-x2=-x+x2⇒f-x≠-fxHence fx=x-x2 is not odd function cfx=cosx⇒f-x=cos-x=cosx=fx⇒f-x≠-fxHence fx=cosx is not odd function dfx=x-x36+x540⇒f-x=-x--x36+-x540=-x+x36-x540=-x-x36+x540=-fx⇒f-x=-fxHence fx=x-x36+x540 is an odd function Hence optiond is correct Hope this information will clear your doubts about this topic If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible Regards

Example 12

Example 12 rutor of •lexive. again m The period of tan x is n so perirud of tan (2n + 3) W2. If fix) = Isin xl then + = Isin (x + Isin = fix). Thus the period offis r. Example 12: Which of the following functions is an function (c) y = cosx Ans. (d) r of 2. 6 40 O Solution: If fix) = — 2r2 thenfl—x) — x' - 2r: = Ax). Hence fis an even function. If u(x) = x ad -x) = x — so u is neither even nor an odd functi cos x. A—x) cos(—x) = cos x = p(x) so p is e 6 40 6 41

Dear Student,
Please find below the solution to the asked query:

A function is odd function if f (- x) = - f (x) (a) f (x) = x^{4} - 2 x^{2} \Rightarrow f (- x) = {(- x)}^{4} - 2 {(- x)}^{2} = x^{4} - 2 x^{2} = f (x) \Rightarrow f (- x) \neq - f (x) Hence f (x) = x^{4} - 2 x^{2} is not odd function . (b) f (x) = x - x^{2} \Rightarrow f (- x) = - x - {(- x)}^{2} = - x - x^{2} = - (x + x^{2}) \Rightarrow f (- x) \neq - f (x) Hence f (x) = x - x^{2} is not odd function . (c) f (x) = cosx \Rightarrow f (- x) = \cos (- x) = cosx = f (x) \Rightarrow f (- x) \neq - f (x) Hence f (x) = cosx is not odd function . (d) f (x) = x - \frac{x^{3}}{6} + \frac{x^{5}}{40} \Rightarrow f (- x) = - x - \frac{{(- x)}^{3}}{6} + \frac{{(- x)}^{5}}{40} = - x + \frac{x^{3}}{6} - \frac{x^{5}}{40} = - (x - \frac{x^{3}}{6} + \frac{x^{5}}{40}) = - f (x) \Rightarrow f (- x) = - f (x) Hence f (x) = x - \frac{x^{3}}{6} + \frac{x^{5}}{40} is an odd function . Hence option (d) is correct .

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

View Full Answer