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})

f (x) = 2 x^{2} - 4 x + 7

f (x) = 3 x^{\frac{1}{5}} - 4

f (x) = 4 x - 13

y = (x - 2)^{2} + 3

f (x) = 10 x + 14

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)