What is the inverse of s/(s^2+1) ?

The inverse of s/(s^2+1) is (1+sqrt(1-4s^2))/(2s),(1-sqrt(1-4s^2))/(2s)

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inverse of s/(s^2+1)

inverse

\frac{s}{s ^{2} + 1}

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

Solution steps

y = \frac{s}{s ^{2} + 1}

Replace

s

with

y

s = \frac{y}{y ^{2} + 1}

Solve for

y, s = \frac{y}{y ^{2} + 1}

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

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