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

The function $'f'$ is defined by $f(x) = x^p (1 - x)^q$ for all $x \in R$, where $p,q$ are positive integers, has a maximum value, for $x$ equal to

The differential equation of the ellipse $\frac{\text{x}^{2}}{\text{a}^{2}}+\frac{\text{y}^{2}}{\text{b}^{2}}=\text{C}$ is:

If $a = 2\,i + 2\,j + 3\,k,\,\,b = - i + 2\,j + k$ and $c = 3\,i + j,$ then $a + t\,b$ is perpendicular to $c$ if $t = $

If $A_1, A_3, ..... A_{2n - 1}$ are $n$ skew symmetric matrices of same order then $B =$$\sum\limits_{r = 1}^n {(2r - 1){{({A_{2r - 1}})}^{2r - 1}}} $ will be

If $F(x)=f(x)+f (\frac {1}{x})$, where $F(x)= \mathop \smallint \limits_{1 }^x \frac {log\, t}{1+t}$ then $F\left( e \right) = $ .

The solution of the differential equation $x\frac{{dy}}{{dx}} + y = {x^2} + 3x + 2$ is

The area of the region bounded by the curve $y=x^2$ and line $y=4$ is:

$\int_{ - \,\pi }^{\,\pi } {\frac{{2x(1 + \sin x)}}{{1 + {{\cos }^2}x}}dx} $ is

Let $f(x) = x^2$ and $g(x) = 2^x.$ Then, the solution set of the equation $fog(x) = gof(x)$ is:

If $y = 2 sin x + sin 2 x$ for $0 \le x \le 2 \pi ,$ then the area enclosed by the curve and the $x-$ axis is