f : R (-1,1), f(x) = e^x - 1 e^x + 1 is - Vidyadip

MCQ

$f : R \rightarrow (-1,1), f(x) = \frac{e^x - 1}{e^x + 1}$ is

A
one-one into
✓
one-one onto
C
many one into
D
many-one onto

✓

Answer

Correct option: B.

one-one onto

b
$f(x)=1-\frac{2}{e^{x}+1}$

range of $f(x)=(-1,1)$

$f^{\prime}(x)=+\frac{2 e^{x}}{\left(e^{x}+1\right)^{2}}>0 \forall x \in R$

so $f(x)$ is one-one onto

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 STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If the position vectors of $ A, B, C, D$ are $2\,i + j,$ $i - 3\,j,$ $3\,i + 2\,j$ and $i + \lambda j$ respectively and $\overrightarrow {AB} ||\overrightarrow {CD} $ , then $\lambda $ will be

If $A$ is a square matrix of order $3$ such that $ \operatorname{det}(\mathrm{A})=3 \text { and } $ $ \operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2 \mathrm{~A})^{-1}\right)\right)\right)\right)\right)=2^{\mathrm{m}} 3^{\mathrm{n}},$ then $m+\mid 2 n$ is equal to:

The xy-plane divided the line joining the point (-1, 3, 4) and (2, -5, 6)

Area lying between the parabola $y^2 = 4x$ and its latus rectum is:

Consider the following statements:Statement $I:\ $ The area bounded by the curve, $\text{y}=\sin\text{x}$ between $\text{x}=0$ and $x = 2p$ is $2\ sq.$ units.Statement $II:\ $ The area bounded by the curve, $\text{y}=2\cos\text{x}$ and the $x-$axis from $\text{x}=0$ to $x = 2p$ is $8\ sq.$ units.

If $\text{A}=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ \text{a} & \text{b} & 2 \end{bmatrix},$ then $aI + bA + 2 A^2$ equals:

If $\displaystyle \text{a}_{\text{ij}}=0\left (\text{i}\neq \text{j} \right )$ and $\displaystyle\text{a}_{\text{ij}}=2\left (\text{i= j} \right )$ then the matrix $\text{A}=\displaystyle \left [ \text{a}_{\text{ij}} \right ]_{\text{n}\times\text{n}}$ is a _______ matrix ?

If $x^y=e^{x-y}$ then $\frac{\text{dy}}{\text{dx}}$ is :

$A B C D$ is a rhombus whose diagonals intersects at $E$. Then $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$ equals to

If $f(x) = 2{x^6} + 3{x^4} + 4{x^2}$ then $f'(x)$ is