Find the domain of fx-ex-e-x2

f(x)=e^x e^ x4 f(x) is defined for all values of x. ...

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Definition of Functions

Find the doma...

Question

Find the domain of
$f (x) = \frac{e^{x} - e^{- x}}{2}$

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Solution

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

f (x) = \frac{e^{x} - e^{| x |}}{e^{x} + e^{| x |}}

f (x) = \frac{e^{x} + e^{- x}}{2}

f (x)

f : R \to (0, 2)

f (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} + 1

f^{- 1}

f (x) = \frac{e^{x} - e^{| x |}}{e^{x} + e^{| x |}}

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