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

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

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

inverse

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

ln (\frac{- 1 + 1 + 8 x}{4}), ln (\frac{- 1 - 1 + 8 x}{4})

Solution steps

y = e^{x} + 2 e^{2 x}

Replace

x

with

y

x = e^{y} + 2 e^{2 y}

Solve for

y, x = e^{y} + 2 e^{2 y}

ln (\frac{- 1 + 1 + 8 x}{4}), ln (\frac{- 1 - 1 + 8 x}{4})

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