What is the inverse of f(x)=(-x)/(x^2+1) ?

The inverse of f(x)=(-x)/(x^2+1) is (-1+sqrt(1-4x^2))/(2x),(-1-sqrt(1-4x^2))/(2x)

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inverse of f(x)=(-x)/(x^2+1)

inverse

f (x) = \frac{- x}{x ^{2} + 1}

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

Solution steps

y = \frac{- x}{x ^{2} + 1}

Replace

x

with

y

x = \frac{- y}{y ^{2} + 1}

Solve for

y, x = \frac{- y}{y ^{2} + 1}

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

What is the inverse of f(x)=(-x)/(x^2+1) ?
The inverse of f(x)=(-x)/(x^2+1) is (-1+sqrt(1-4x^2))/(2x),(-1-sqrt(1-4x^2))/(2x)