If f(x) = 1 + x 1 - x , then f(x) is - Vidyadip

MCQ

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

✓

Answer

Correct option: D.

Odd function

d
(d) Here, $f(x) = \log \left( {\frac{{1 + x}}{{1 - x}}} \right)$

and $f( - x) = \log \left( {\frac{{1 - x}}{{1 + x}}} \right) = \log {\left( {\frac{{1 + x}}{{1 - x}}} \right)^{ - 1}}$

$ = - \log \left( {\frac{{1 + x}}{{1 - x}}} \right) = - f(x)$ ==> $f(x)$ is an odd function.

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

Explore more

More "M.C.Q (1 Marks)" from 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The integral $16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}$ is equal to

The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x - 5y + 2z = 11 is given by:

3x - 5y + 2z - 13 = 0
5x - 3y + 2z + 13 = 0
3x - 2y + 5z + 13 = 0
3x - 5y + 2z + 13 = 0

$\int_{\, - 1}^{\,2} {|x|\,dx} =$

If $\int_{}^{} {\sin 5x\cos 3x\;dx = - \frac{{\cos 8x}}{{16}}} + A$, then $A = $

If the function $f(x) = \left\{ \begin{array}{l}
{\tan ^{ - 1}}x;x < 1\\
{\sec ^{ - 1}}x + \lambda ;x \ge 1
\end{array} \right.$ has local minima at $x = 1$, then range of $\lambda$ is-

An are $P Q$ of a circle subtends a right angle at its centre $O$. The mid point of the arc $P Q$ is $R$. If $\overline{O P}=\vec{u}, \overline{O R}=\vec{v}$ and $\overrightarrow{O Q}=\alpha \vec{u}+\beta \vec{v}$, then $\alpha, \beta^2$ are the roots of the equation

Let $a, b, c \in R$ be all non-zero and satisfy $a^{3}+b^{3}+c^{3}=2 .$ If the matrix $A=\left(\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right)$ satisfies $\mathrm{A}^{\mathrm{T}} \mathrm{A}=\mathrm{I},$ then a value of $abc$ can be

If $f(x) = {1 \over {1 - x}}$, then the derivative of the composite function $f[f\{ f(x)\} ]$ is equal to

The area bounded by the curve y = (x + 1)², y = (x - 1)² and the line y = 0 is:

$\frac{1}{6}$
$\frac{2}{3}$
$\frac{1}{4}$
$\frac{1}{3}$

The period of function

$f\left( x \right) = {\cos ^2}\left( {\sin x} \right) + {\sin ^2}\left( {\cos x} \right)$ is