What is the inverse of f(x)=(10e^{2x}+8)/(4+e^{2x)} ?

The inverse of f(x)=(10e^{2x}+8)/(4+e^{2x)} is (ln((8-4x)/(x-10)))/2

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inverse of f(x)=(10e^{2x}+8)/(4+e^{2x)}

inverse

f (x) = \frac{10 e ^{2 x} + 8}{4 + e ^{2 x}}

\frac{ln ( \frac{8 - 4 x}{x - 10} )}{2}

Solution steps

y = \frac{10 e ^{2 x} + 8}{4 + e ^{2 x}}

Replace

x

with

y

x = \frac{10 e ^{2 y} + 8}{4 + e ^{2 y}}

Solve for

y, x = \frac{10 e ^{2 y} + 8}{4 + e ^{2 y}}

\frac{ln ( \frac{8 - 4 x}{x - 10} )}{2}

What is the inverse of f(x)=(10e^{2x}+8)/(4+e^{2x)} ?
The inverse of f(x)=(10e^{2x}+8)/(4+e^{2x)} is (ln((8-4x)/(x-10)))/2