What is the inverse of f(x)=200ln((400)/(500-x))+100 ?

The inverse of f(x)=200ln((400)/(500-x))+100 is -(400-500e^{\frac{x-100)/(200)}}{e^{(x-100)/(200)}}

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inverse of f(x)=200ln((400)/(500-x))+100

inverse

f (x) = 200 ln (\frac{400}{500 - x}) + 100

- \frac{400 - 500 e ^{\frac{x - 100}{200}}}{e ^{\frac{x - 100}{200}}}

Solution steps

y = 200 ln (\frac{400}{500 - x}) + 100

Replace

x

with

y

x = 200 ln (\frac{400}{500 - y}) + 100

Solve for

y, x = 200 ln (\frac{400}{500 - y}) + 100

- \frac{400 - 500 e ^{\frac{x - 100}{200}}}{e ^{\frac{x - 100}{200}}}

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What is the inverse of f(x)=200ln((400)/(500-x))+100 ?
The inverse of f(x)=200ln((400)/(500-x))+100 is -(400-500e^{\frac{x-100)/(200)}}{e^{(x-100)/(200)}}