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

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

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inverse of f(x)=1+e^{1+sqrt(1-x)}

inverse

f (x) = 1 + e^{1 + 1 - x}

- ln^{2} (x - 1) + 2 ln (x - 1)

Solution steps

y = 1 + e^{1 + 1 - x}

Replace

x

with

y

x = 1 + e^{1 + 1 - y}

Solve for

y, x = 1 + e^{1 + 1 - y}

- ln^{2} (x - 1) + 2 ln (x - 1)

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