What is the inverse of f(x)=e^x+1/(e^x) ?

The inverse of f(x)=e^x+1/(e^x) is ln((x+sqrt(x^2-4))/2),ln((x-sqrt(x^2-4))/2)

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inverse of f(x)=e^x+1/(e^x)

inverse

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

ln (\frac{x + x ^{2} - 4}{2}), ln (\frac{x - x ^{2} - 4}{2})

Solution steps

y = e^{x} + \frac{1}{e ^{x}}

Replace

x

with

y

x = e^{y} + \frac{1}{e ^{y}}

Solve for

y, x = e^{y} + \frac{1}{e ^{y}}

ln (\frac{x + x ^{2} - 4}{2}), ln (\frac{x - x ^{2} - 4}{2})

y = - \frac{2}{5} x + 3

f (x) = 3 (x + 2)^{3} - 1

\frac{1}{x} + 2

\frac{1}{x} + 4

f (x) = x^{\frac{3}{5}} + 2

What is the inverse of f(x)=e^x+1/(e^x) ?
The inverse of f(x)=e^x+1/(e^x) is ln((x+sqrt(x^2-4))/2),ln((x-sqrt(x^2-4))/2)