What is the inverse of 1/4 ln((x-2)/(x+1)) ?

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

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inverse of 1/4 ln((x-2)/(x+1))

inverse

\frac{1}{4} ln (\frac{x - 2}{x + 1})

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

Solution steps

y = \frac{1}{4} ln (\frac{x - 2}{x + 1})

Replace

x

with

y

x = \frac{1}{4} ln (\frac{y - 2}{y + 1})

Solve for

y, x = \frac{1}{4} ln (\frac{y - 2}{y + 1})

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

f (x) = e^{3 x + 4}

f (x) = x^{2} - 12 x + 36, x \geq 6

f (x) = - x 3 + 6 x 2 - 9 x

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

f (x) = \frac{7 x - 6}{4 x + 3}

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