First slide

Introduction to real valued functions

Question

The inverse of the function
$f (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} + 2$ is given by

Moderate

A

$\log_{e} {(\frac{x - 1}{x + 1})}^{- 2}$
B

$\log_{e} {(\frac{x - 2}{x - 1})}^{1 / 2}$
C

$\log_{e} {(\frac{x}{2 - x})}^{1 / 2}$
D

$\log_{e} {(\frac{x - 1}{3 - x})}^{1 / 2}$

Solution

Let y = f(x) $\Rightarrow y - 2 = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} a p p l y c o m p o d e n d o d i v e d e n d o \frac{y - 1}{y - 3} = \frac{2 e^{x}}{2 e^{- x}}$

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