What is the inverse of log_{e}((2-x)/(x+3)) ?

The inverse of log_{e}((2-x)/(x+3)) is (2-3e^x)/(e^x+1)

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inverse of log_{e}((2-x)/(x+3))

inverse

lo g_{e} (\frac{2 - x}{x + 3})

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

Solution steps

y = lo g_{e} (\frac{2 - x}{x + 3})

Replace

x

with

y

x = lo g_{e} (\frac{2 - y}{y + 3})

Solve for

y, x = lo g_{e} (\frac{2 - y}{y + 3})

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

f (x) = 3 - x

f (x) = (12 - x)^{\frac{1}{4}}

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

f (x) = - 3 - x + 2

2 x^{2} + 5 x - 3

What is the inverse of log_{e}((2-x)/(x+3)) ?
The inverse of log_{e}((2-x)/(x+3)) is (2-3e^x)/(e^x+1)