MCQ
Which of the following is an even function :-
  • A
    $f(x) = \log \left( {\frac{{1 - x}}{{1 + x}}} \right)$
  • B
    $f(x) = \left\{ {{x^3} + \sqrt {1 + {x^6}} } \right\}$
  • $f(x) = \frac{x}{{{2^x} - 1}} + \frac{x}{2} + 1$
  • D
    $f(x) = {e^{5x}} + \sin 7x$

Answer

Correct option: C.
$f(x) = \frac{x}{{{2^x} - 1}} + \frac{x}{2} + 1$
c

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are
The angle between a line with direction ratios $2 : 2 : 1$ and a line joining $(3, 1, 4)$ to $(7, 2, 12)$ is
If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
  {{b^5}{c^6}\left( {{c^3} - {b^3}} \right)}&{{a^4}{c^6}\left( {{a^3} - {c^3}} \right)}&{{a^4}{b^5}\left( {{b^3} - {a^3}} \right)} \\ 
  {{b^2}{c^3}\left( {{b^6} - {c^6}} \right)}&{a{c^3}\left( {{c^6} - {a^6}} \right)}&{a{b^2}\left( {{a^6} - {b^6}} \right)} \\ 
  {{b^2}{c^3}\left( {{c^3} - {b^3}} \right)}&{a{c^3}\left( {{a^3} - {c^3}} \right)}&{a{b^2}\left( {{b^3} - {a^3}} \right)} 
\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{*{20}{c}}
  a&{{b^2}}&{{c^3}} \\ 
  {{a^4}}&{{b^5}}&{{c^6}} \\ 
  {{a^7}}&{{b^8}}&{{c^9}} 
\end{array}} \right|$ then ${\Delta _1}{\Delta _2}$ is equal to
Two points $(a, 0)$ and $(0, b)$ are joined by a straight line, Another point on this line is
Let $f: R-\left\{\frac{-1}{2}\right\} \rightarrow R$ and $g: R-\left\{\frac{-5}{2}\right\} \rightarrow R$ be defined as $f ( x )=\frac{2 x +3}{2 x +1}$ and $g ( x )=\frac{| x |+1}{2 x +5}$. Then the domain of the function fog is :
If $\alpha$, $\beta$,$\gamma$ are positive number such that $\alpha + \beta = \pi$  and $\beta  + \gamma = \alpha$, then $tan\ \alpha$ is equal to - (where $\gamma  \ne n\pi ,n \in I$ )
Points $P (-3,2), Q (9,10)$ and $R (\alpha, 4)$ lie on a circle $C$ with $P R$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2 x - ky =1$, then $k$ is equal to $.........$.
The direction cosines of the resultant of the vectors $(i + j + k),$$( - i + j + k),$ $(i - j + k)$ and $(i + j - k),$ are
The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to
If $z = \frac{{\sqrt 3 }}{2} + \frac{i}{2}\,\,\,\left( {i = \sqrt { - 1} } \right)$, then ${\left( {1 + iz + {z^5} + i{z^8}} \right)^9}$ is equal to