What is the inverse of S/(S^2+4S+5) ?

The inverse of S/(S^2+4S+5) is (-4S+1+sqrt(-4S^2-8S+1))/(2S),(-4S+1-sqrt(-4S^2-8S+1))/(2S)

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inverse of S/(S^2+4S+5)

inverse

\frac{S}{S ^{2} + 4 S + 5}

\frac{- 4 S + 1 + - 4 S ^{2} - 8 S + 1}{2 S}, \frac{- 4 S + 1 - - 4 S ^{2} - 8 S + 1}{2 S}

Solution steps

y = \frac{S}{S ^{2} + 4 S + 5}

Replace

S

with

y

S = \frac{y}{y ^{2} + 4 y + 5}

Solve for

y, S = \frac{y}{y ^{2} + 4 y + 5}

\frac{- 4 S + 1 + - 4 S ^{2} - 8 S + 1}{2 S}, \frac{- 4 S + 1 - - 4 S ^{2} - 8 S + 1}{2 S}

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

f (x) = (x + 3)^{2} - 1, x \geq - 3

f (x) = 12 + 2 x - 2

f (x) = 8 x, x > 4

f (x) = \frac{2}{x - 1} - 4

What is the inverse of S/(S^2+4S+5) ?
The inverse of S/(S^2+4S+5) is (-4S+1+sqrt(-4S^2-8S+1))/(2S),(-4S+1-sqrt(-4S^2-8S+1))/(2S)