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Question

The function f(x)=sinlogx+x2+1, is(1) An even function(2) An odd function(3) A periodic function(4) Neither odd nor even function

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Solution

fx=sinlogx+x2+1Let gx=logx+x2+1g-x=log-x+-x2+1g-x=log-x+x2+1g-x=logx2+1-x×x2+1+xx2+1+xg-x=logx2+12-x2x2+1+xg-x=logx2+1-x2x2+1+xg-x=log1x2+1+xUse logamn=logam-logang-x=log 1-log x2+1+xg-x=-log x2+1+xg-x=-gxNowfx=sinlogx+x2+1fx=singxf-x=sing-x=sin-gx=-singx=-fxHence fx is odd

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