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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The function $f (x)=\sec \left[\log \left(x+\sqrt{1+x^2}\right)\right]$ is
  • A
    Odd
  • ✓
    Even
  • C
    Neither odd not even
  • D
    Constant
✓

Answer

Correct option: B.
Even
(B)
$f (-x)=\sec \left[\log \left(-x+\sqrt{1+(-x)^2}\right)\right]$
$=\sec \left[\log \left(-x+\sqrt{1+x^2}\right)\right]$
$=\sec \left[\log \left(\sqrt{1+x^2}-x\right)\right]$
$=\sec \left[\log \left(\frac{1+x^2-x^2}{\sqrt{1+x^2}+x}\right)\right]$
$=\sec \left[\log \left(\frac{1}{\sqrt{1+x^2}+x}\right)\right]$
$=\sec \left[-\log \left(\sqrt{1+x^2}+x\right)\right]$
$=\sec \left[\log \left(\sqrt{1+x^2}+x\right)\right]$
$\therefore f (x)$ is an even function.

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