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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
Which of the following functions is an odd function?
  • ✓
    $f (x)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$
  • B
    $f (x)=x\left(\frac{ a ^x+1}{ a ^x-1}\right)$
  • C
    $f (x)=\log _{10}\left(\frac{1-x^2}{1+x^2}\right)$
  • D
    $f (x)= k ($ constant $)$
✓

Answer

Correct option: A.
$f (x)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$
(A)
Let $f (x)=\sqrt{1+x+x^2}-\sqrt{1-x+x^2}$, then
$f (-x)=\sqrt{1-x+x^2}-\sqrt{1+x+x^2}$
Here, $f (-x)=- f (x)$
$\therefore f (x)$ is an odd function.

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