If $f(x) = \log \frac{{1 + x}}{{1 - x}}$, then $f(x)$ is

  • A

    Even function

  • B

    $f({x_1})f({x_2}) = f({x_1} + {x_2})$

  • C

    $\frac{{f({x_1})}}{{f({x_2})}} = f({x_1} - {x_2})$

  • D

    Odd function

Similar Questions

A function $f(x)$ is given by $f(x)=\frac{5^{x}}{5^{x}+5}$, then the sum of the series

$f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right)$ is equal to ....... .

  • [JEE MAIN 2021]

If $f(x)$ is a quadratic expression such that $f(1) + f (2)\, = 0$ , and $-1$ is a root of $f(x)\, = 0$, then the other root of $f(x)\, = 0$ is

  • [JEE MAIN 2018]

If $f(x) = \log \left[ {\frac{{1 + x}}{{1 - x}}} \right]$, then $f\left[ {\frac{{2x}}{{1 + {x^2}}}} \right]$ is equal to

Prove that the function $f: R \rightarrow R$, given by $f(x)=2 x,$ is one-one and onto.

If in greatest integer function, the domain is a set of real numbers, then range will be set of