What is the inverse of f(x)=ln(1/(3-x)) ?

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

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inverse of f(x)=ln(1/(3-x))

inverse

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

- \frac{1 - 3 e ^{x}}{e ^{x}}

Solution steps

y = ln (\frac{1}{3 - x})

Replace

x

with

y

x = ln (\frac{1}{3 - y})

Solve for

y, x = ln (\frac{1}{3 - y})

- \frac{1 - 3 e ^{x}}{e ^{x}}

\frac{x ^{2}}{x ^{2} - 1}

f (x) = 5 x^{2} + 10 x + 20

f (x) = 3.2

f (x) = \frac{x + 3}{x + 8}

f (x) = x - 5 - 2

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