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

The inverse of f(x)=e^{2x}-6e^x+5 is ln(3+sqrt(x+4)),ln(3-sqrt(x+4))

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

inverse

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

ln (3 + x + 4), ln (3 - x + 4)

Solution steps

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

Replace

x

with

y

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

Solve for

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

ln (3 + x + 4), ln (3 - x + 4)

What is the inverse of f(x)=e^{2x}-6e^x+5 ?
The inverse of f(x)=e^{2x}-6e^x+5 is ln(3+sqrt(x+4)),ln(3-sqrt(x+4))