The inverse of the function 10 ^x - 10 ^ - x 10 ^x + 10 ^ - x is - Vidyadip

MCQ

The inverse of the function $\frac{{{{10}^x} - {{10}^{ - x}}}}{{{{10}^x} + {{10}^{ - x}}}}$ is

✓
$\frac{1}{2}{\log _{10}}\left( {\frac{{1 + x}}{{1 - x}}} \right)$
B
$\frac{1}{2}{\log _{10}}\left( {\frac{{1 - x}}{{1 + x}}} \right)$
C
$\frac{1}{4}{\log _{10}}\left( {\frac{{2x}}{{2 - x}}} \right)$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{2}{\log _{10}}\left( {\frac{{1 + x}}{{1 - x}}} \right)$

a
(a) $y = \frac{{{{10}^x} - {{10}^{ - x}}}}{{{{10}^x} + {{10}^{ - x}}}}$

$\Rightarrow x = \frac{1}{2}{\log _{10}}\left( {\frac{{1 + y}}{{1 - y}}} \right)$

Let $y = f(x)$ ==> $x = \pi ,\,\,f(\pi ) = - \tan \frac{\pi }{4} = - 1$

==> ${f^{ - 1}}(y) = \frac{1}{2}{\log _{10}}\left( {\frac{{1 + y}}{{1 - y}}} \right)$

==>${f^{ - 1}}(x) = \frac{1}{2}{\log _{10}}\left( {\frac{{1 + x}}{{1 - x}}} \right)$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\alpha \in (0, \pi /2)$ be fixed. If the integral $\int {\frac{{\tan \,x + \tan \,\alpha }}{{\tan \,x - \tan \,\alpha }}dx = A\left( x \right)\,\cos \,2\alpha + B\left( x \right)\,\sin \,2\alpha + C} $ where $C$ is a constant of integration, then the functions $A(x)$ and $B(x)$ are respectively

How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

The value of the integral $\int_{ - \pi /4}^{\pi /4} {{{\sin }^{ - 4}}x} \,dx$ is

If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to

${\tan ^{ - 1}}\frac{x}{{\sqrt {{a^2} - {x^2}} }} = $

General solution of $eq^n\, 2tan\theta \, -\, cot\theta =\, -1$ is

If $m$ is a non-zero number and $\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c$ , then $f(x)$ is

Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$

The differential equation of the family of parabolas with focus at the origin and the $x$-axis as axis is

The number of elements in the set $S=$ $\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.$ $\left.10 \cos ^{2} \theta+5=0\right\}$ is