What is the inverse of f(x)=(e^{-3x}+4)/2+1 ?

The inverse of f(x)=(e^{-3x}+4)/2+1 is -(ln(2x-6))/3

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inverse of f(x)=(e^{-3x}+4)/2+1

inverse

f (x) = \frac{e ^{- 3 x} + 4}{2} + 1

- \frac{ln ( 2 x - 6 )}{3}

Solution steps

y = \frac{e ^{- 3 x} + 4}{2} + 1

Replace

x

with

y

x = \frac{e ^{- 3 y} + 4}{2} + 1

Solve for

y, x = \frac{e ^{- 3 y} + 4}{2} + 1

- \frac{ln ( 2 x - 6 )}{3}

f (x) = \frac{x ^{2} - 2 x - 15}{x ^{2} - 4}

f (x) = \frac{4}{3 x + 5}

f (x) = x^{2} - 9, x > 0

f (x) = \frac{1}{4} ln (\frac{1}{3} x)

f (x) = \frac{2 e ^{x} - 10}{22 e ^{x} + 14}

What is the inverse of f(x)=(e^{-3x}+4)/2+1 ?
The inverse of f(x)=(e^{-3x}+4)/2+1 is -(ln(2x-6))/3