If f(x) = 1 - x 1 + x , then f[f( ;2 )] = - Vidyadip

MCQ

If $f(x) = \frac{{1 - x}}{{1 + x}},$ then $f[f(\cos \;2\theta )] = $

A
$\tan 2\theta $
B
$\sec 2\theta $
✓
$\cos 2\theta $
D
$\cot 2\theta $

✓

Answer

Correct option: C.

$\cos 2\theta $

c
(c) $f[f(\cos \,\,2\theta )] = f\,\left[ {\frac{{1 - \cos \,\,2\theta }}{{1 + \cos \,\,2\theta }}} \right]$

$ = f({\tan ^2}\theta ) = \frac{{1 - {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }} = \cos \,\,2\theta .$

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

If magnitude of sum of two unit vectors is greater than magnitude of their difference and less than $\sqrt 3$ times of magnitude of their difference then complete set, where angle between the vectors lies, is

The derivative of $F(x) = \int_{{x^2}}^{{x^3}} {\frac{1}{{\log t}}\,dt} $, $(x > 0)$ is

If $f (x) = 1 + x +\int\limits_1^x {\left( {\,{{\ln }^2}t\, + \,2\ln t\,} \right)\,dt} $ , then $f (x)$ increases in

If $F(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$ and $[F(x)]^2=F(k x)$, then the value of $k$ is :

Let the vectors $\vec{a}, \vec{b}, \vec{c}$ represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by $\vec{a}, \vec{b}+\vec{c}$ and $\vec{a}+2 \vec{b}+3 \vec{c}$ is equal to $..........\,V$

Let $a ,b ,c $ be such that $b + c \ne 0$ if

$\left| {\begin{array}{*{20}{c}}a&{a + 1}&{a - 1}\\{ - b}&{b + 1}&{b - 1}\\c&{c - 1}&{c + 1}\end{array}} \right| + \left| {\begin{array}{*{20}{c}}{a + 1}&{b + 1}&{c - 1}\\{a - 1}&{b - 1}&{c + 1}\\{{{\left( { - 1} \right)}^{n + 2}} \cdot a}&{{{\left( { - 1} \right)}^{n + 1}} \cdot b}&{{{\left( { - 1} \right)}^n} \cdot c}\end{array}} \right| = 0$ then $n$ equals to

The sum of the maximum and minimum values of the function $f(x)=|5 x-7|+\left[x^{2}+2 x\right]$ is the interval $\left[\frac{5}{4}, 2\right]$, where $[ t ]$ is the greatest integer $\leq t$ is $.......$

The set of all real values of $\lambda$ for which the function $f(x)=\left(1-\cos ^{2} x\right) \cdot(\lambda+\sin x)$ $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right),$ has exactly one maxima and exactly one minima, is

Let $A$ be the region enclosed by the parabola $y^2=2 x$ and the line $x=24$. Then the maximum area of the rectangle inscribed in the region $\mathrm{A}$ is ..................

If $\left(\sin ^{-1} x\right)^{2}-\left(\cos ^{-1} x\right)^{2}=a ; 0\,<\,x\,<\,1, a \neq 0$, then the value of $2 \mathrm{x}^{2}-1$ is :