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AP EAMCET202423 May 2024Morning ShiftMathematicsFunctionsActual

Which of the following functions are odd? I. f(x)=x ( e^x-1 e^x+1 ) II. f(x)=k^x+k^ -x + x III. f(x)= (x+ x^2+1 )

Options

  1. AII
  2. BI, II
  3. CIII
  4. DI

Correct answer

C. III

Step-by-step solution

III. Since, f(x)= (x+ x^2+1 ) aligned & f(-x)= (-x+ x^2+1 ) & =- ( 1 ( 1+x^2 -x . 1+x^2 +x ( 1+x^2 +x ) )=- (x+ x^2+1 ) & f(-x)=-f(x) So, f(x) is odd function. aligned

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