What is the inverse of (1-2s)/(s^2+4s+5) ?

The inverse of (1-2s)/(s^2+4s+5) is (-2s-1+sqrt(-s^2+5s+1))/s ,-(2s+sqrt(-s^2+5s+1)+1)/s

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inverse of (1-2s)/(s^2+4s+5)

inverse

\frac{1 - 2 s}{s ^{2} + 4 s + 5}

\frac{- 2 s - 1 + - s ^{2} + 5 s + 1}{s}, - \frac{2 s + - s ^{2} + 5 s + 1 + 1}{s}

Solution steps

y = \frac{1 - 2 s}{s ^{2} + 4 s + 5}

Replace

s

with

y

s = \frac{1 - 2 y}{y ^{2} + 4 y + 5}

Solve for

y, s = \frac{1 - 2 y}{y ^{2} + 4 y + 5}

\frac{- 2 s - 1 + - s ^{2} + 5 s + 1}{s}, - \frac{2 s + - s ^{2} + 5 s + 1 + 1}{s}

- 3 (y + 2)^{2} + 1

f (x) = 2 π r^{2} + 2 π r

f (x) = - \frac{2 x}{3} - 6

f (x) = \frac{5 x - 2}{3 + 8 x}

2 3 x - 3

What is the inverse of (1-2s)/(s^2+4s+5) ?
The inverse of (1-2s)/(s^2+4s+5) is (-2s-1+sqrt(-s^2+5s+1))/s ,-(2s+sqrt(-s^2+5s+1)+1)/s