What is the inverse of f(x)=(s+1)/(s^2+s-6) ?

The inverse of f(x)=(s+1)/(s^2+s-6) is (-s+1+sqrt(25s^2+2s+1))/(2s),(-s+1-sqrt(25s^2+2s+1))/(2s)

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inverse of f(x)=(s+1)/(s^2+s-6)

inverse

f (x) = \frac{s + 1}{s ^{2} + s - 6}

\frac{- s + 1 + 25 s ^{2} + 2 s + 1}{2 s}, \frac{- s + 1 - 25 s ^{2} + 2 s + 1}{2 s}

Solution steps

x = \frac{s + 1}{s ^{2} + s - 6}

Replace

s

with

x

s = \frac{x + 1}{x ^{2} + x - 6}

Solve for

x, s = \frac{x + 1}{x ^{2} + x - 6}

\frac{- s + 1 + 25 s ^{2} + 2 s + 1}{2 s}, \frac{- s + 1 - 25 s ^{2} + 2 s + 1}{2 s}

f (x) = x - 915

f (x) = \frac{- 3 x + 4}{2 x - 1}

x^{2} - 9 x + 20

y = \frac{1}{2} (x - 4)^{2} + 1

f (x) = - 3 x^{3} + 4

What is the inverse of f(x)=(s+1)/(s^2+s-6) ?
The inverse of f(x)=(s+1)/(s^2+s-6) is (-s+1+sqrt(25s^2+2s+1))/(2s),(-s+1-sqrt(25s^2+2s+1))/(2s)