What is the inverse of f(x)=(2e^{5x}-6)/(5e^{5x)+2} ?

The inverse of f(x)=(2e^{5x}-6)/(5e^{5x)+2} is (ln((-6-2x)/(5x-2)))/5

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inverse of f(x)=(2e^{5x}-6)/(5e^{5x)+2}

inverse

f (x) = \frac{2 e ^{5 x} - 6}{5 e ^{5 x} + 2}

\frac{ln ( \frac{- 6 - 2 x}{5 x - 2} )}{5}

Solution steps

y = \frac{2 e ^{5 x} - 6}{5 e ^{5 x} + 2}

Replace

x

with

y

x = \frac{2 e ^{5 y} - 6}{5 e ^{5 y} + 2}

Solve for

y, x = \frac{2 e ^{5 y} - 6}{5 e ^{5 y} + 2}

\frac{ln ( \frac{- 6 - 2 x}{5 x - 2} )}{5}

What is the inverse of f(x)=(2e^{5x}-6)/(5e^{5x)+2} ?
The inverse of f(x)=(2e^{5x}-6)/(5e^{5x)+2} is (ln((-6-2x)/(5x-2)))/5