What is the inverse of f(x)=1+e^{1-\sqrt[3]{x}} ?

The inverse of f(x)=1+e^{1-\sqrt[3]{x}} is -ln^3(x-1)+3ln^2(x-1)-3ln(x-1)+1

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inverse of f(x)=1+e^{1-\sqrt[3]{x}}

inverse

- ln^{3} (x - 1) + 3 ln^{2} (x - 1) - 3 ln (x - 1) + 1

Solution steps

y = 1 + e^{1 - 3 x}

Replace

x

with

y

x = 1 + e^{1 - 3 y}

Solve for

y, x = 1 + e^{1 - 3 y}

- ln^{3} (x - 1) + 3 ln^{2} (x - 1) - 3 ln (x - 1) + 1

What is the inverse of f(x)=1+e^{1-\sqrt[3]{x}} ?
The inverse of f(x)=1+e^{1-\sqrt[3]{x}} is -ln^3(x-1)+3ln^2(x-1)-3ln(x-1)+1