CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Inverse of function $$f(x) = \dfrac {10^{x} - 10^{-x}}{10^{x} + 10^{-x}}$$ is


A
log10(2x)
loader
B
12log10(1+x1x)
loader
C
12log10(2x1)
loader
D
12log10(2x2x)
loader

Solution

The correct option is B $$\dfrac {1}{2}\log_{10}\left (\dfrac {1 + x}{1 - x}\right )$$
Let $$f(x) = y$$, then

$$\dfrac {10^{x} - 10^{-x}}{10^{x} + 10^{-x}} = y$$

$$\Rightarrow \dfrac {10^{2x} - 1}{10^{2x} + 1} = y$$

$$\Rightarrow 10^{2x} = \dfrac {1 + y}{1 - y}$$ .... By Componendo and dividendo

$$\Rightarrow x = \dfrac {1}{2}\log_{10}\left (\dfrac {1 + y}{1 - y}\right )$$

$$\Rightarrow f^{-1}(y) = \dfrac {1}{2}\log_{10}\left (\dfrac {1 + y}{1 - y}\right )$$

$$\therefore f^{-1} (x) = \dfrac {1}{2}\log_{10}\left (\dfrac {1 + x}{1 - x}\right )$$.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image