What is the inverse of f(x)=2-e^{(-1/3 y)} ?

The inverse of f(x)=2-e^{(-1/3 y)} is -3ln(2-y)

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inverse of f(x)=2-e^{(-1/3 y)}

inverse

f (x) = 2 - e^{(- \frac{1}{3} y)}

- 3 ln (2 - y)

Solution steps

x = 2 - e^{- \frac{1}{3} y}

Replace

y

with

x

y = 2 - e^{- \frac{1}{3} x}

Solve for

x, y = 2 - e^{- \frac{1}{3} x}

- 3 ln (2 - y)

f (x) = x + 5 - 8

y = \frac{3 x - 4}{2 - x}

f (x) = 6 x^{2} - 12 x + 1

f (x) = 3 (x + 8)^{7} - 7

f (x) = \frac{8}{2 x - 1}

What is the inverse of f(x)=2-e^{(-1/3 y)} ?
The inverse of f(x)=2-e^{(-1/3 y)} is -3ln(2-y)