What is the inverse of 2e^x-1/(e^x) ?

The inverse of 2e^x-1/(e^x) is ln((x+sqrt(x^2+8))/4),ln((x-sqrt(x^2+8))/4)

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inverse of 2e^x-1/(e^x)

inverse

2 e^{x} - \frac{1}{e ^{x}}

ln (\frac{x + x ^{2} + 8}{4}), ln (\frac{x - x ^{2} + 8}{4})

Solution steps

y = 2 e^{x} - \frac{1}{e ^{x}}

Replace

x

with

y

x = 2 e^{y} - \frac{1}{e ^{y}}

Solve for

y, x = 2 e^{y} - \frac{1}{e ^{y}}

ln (\frac{x + x ^{2} + 8}{4}), ln (\frac{x - x ^{2} + 8}{4})

y = 2 x^{5}

f (x) = 3 lo g_{4} (x) - 5

f (x) = \frac{2 x + 4}{x}

f (x) = arcsin (x - 4)

lo g_{10} (2 - x)

What is the inverse of 2e^x-1/(e^x) ?
The inverse of 2e^x-1/(e^x) is ln((x+sqrt(x^2+8))/4),ln((x-sqrt(x^2+8))/4)