What is the inverse of ln((3+2x^2)/(x^2+1)) ?

The inverse of ln((3+2x^2)/(x^2+1)) is sqrt((3-e^x)/(e^x-2)),-sqrt((3-e^x)/(e^x-2))

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inverse of ln((3+2x^2)/(x^2+1))

inverse

ln (\frac{3 + 2 x ^{2}}{x ^{2} + 1})

\frac{3 - e ^{x}}{e ^{x} - 2}, - \frac{3 - e ^{x}}{e ^{x} - 2}

Solution steps

y = ln (\frac{3 + 2 x ^{2}}{x ^{2} + 1})

Replace

x

with

y

x = ln (\frac{3 + 2 y ^{2}}{y ^{2} + 1})

Solve for

y, x = ln (\frac{3 + 2 y ^{2}}{y ^{2} + 1})

\frac{3 - e ^{x}}{e ^{x} - 2}, - \frac{3 - e ^{x}}{e ^{x} - 2}

What is the inverse of ln((3+2x^2)/(x^2+1)) ?
The inverse of ln((3+2x^2)/(x^2+1)) is sqrt((3-e^x)/(e^x-2)),-sqrt((3-e^x)/(e^x-2))