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

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

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

inverse

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

ln (- 1 + x + 1), ln (- x + 1 - 1)

Solution steps

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

Replace

x

with

y

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

Solve for

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

ln (- 1 + x + 1), ln (- x + 1 - 1)

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