What is the inverse of f(x)=ln(1+e^{2x}) ?

The inverse of f(x)=ln(1+e^{2x}) is (ln(e^x-1))/2

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inverse of f(x)=ln(1+e^{2x})

inverse

f (x) = ln (1 + e^{2 x})

\frac{ln ( e ^{x} - 1 )}{2}

Solution steps

y = ln (1 + e^{2 x})

Replace

x

with

y

x = ln (1 + e^{2 y})

Solve for

y, x = ln (1 + e^{2 y})

\frac{ln ( e ^{x} - 1 )}{2}

f (x) = \frac{x ^{2}}{2} - x - 1

f (x) = 2.5 x + 11.5

f (x) = lo g_{5} (x - 2)

e^{y}

\frac{x + 28}{x - 7}

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