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

Choose the correct option from given four options:
$\int\frac{\text{x}}{\text{x}+1}$ is equal to:
  1. $\text{x}+\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
  2. $\text{x}+\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{C}$
  3. $\text{x}-\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1+\text{x}|+\text{C}$
  4. $\text{x}-\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1+\text{x}|+\text{C}$
The function $f(x) = {{\log x} \over x}$ is increasing in the interval
Let PQR be a triangle. The points $A , B$ and $C$ are on the sides $QR , RP$ and $PQ$ respectively such that $\frac{ QA }{ AR }=\frac{ RB }{ BP }=\frac{ PC }{ CQ }=\frac{1}{2}$. Then $\frac{\operatorname{Area}(\triangle PQR )}{\operatorname{Area}(\triangle ABC )}$ is equal to $........$
In a triangle $\mathrm{ABC}$, if $|\overrightarrow{\mathrm{BC}}|=3,|\overrightarrow{\mathrm{C}}|=5$ and $|\overrightarrow{\mathrm{BA}}|=7$, then the projection of the vector $\overline{\mathrm{BA}}$ on $\overline{\mathrm{BC}}$ is equal to:
If $y = f(x) = \frac{{x + 2}}{{x - 1}}$, then $x = $
If the matrices $A=\left[\begin{array}{ccc}{1} & {1} & {2} \\ {1} & {3} & {4} \\ {1} & {-1} & {3}\end{array}\right], B=\operatorname{adj} A$ and $\mathrm{C}=3 \mathrm{A},$ then $\frac{|\mathrm{adjB}|}{|\mathrm{C}|}$ is equal to
Solve $\tan ^{-1} \frac{1-x}{1+x}=\frac{1}{2} \tan ^{-1} x,(x>0)$
$\int_0^{\pi /2} {\frac{{1 + 2\cos x}}{{{{(2 + \cos x)}^2}}} = } $
Region represented by $\text{x}\geq0, \text{y}\geq0$ is:
  1. First quadrant
  2. Second quadrant
  3. Third quadrant
  4. Fourth quadrant
Volume of the parallelopiped whose coterminous edges are $2i - 3j + 4k,\,\,i + 2j - 2k,\,\,3i - j + k,$ is ............ $\mathrm{cubic\,unit}$