What is the inverse of f(x)= 9/((x^2+5x+6)) ?

The inverse of f(x)= 9/((x^2+5x+6)) is (-5x+sqrt(x^2+36x))/(2x),(-5x-sqrt(x^2+36x))/(2x)

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inverse of f(x)= 9/((x^2+5x+6))

inverse

f (x) = \frac{9}{( x ^{2} + 5 x + 6 )}

\frac{- 5 x + x ^{2} + 36 x}{2 x}, \frac{- 5 x - x ^{2} + 36 x}{2 x}

Solution steps

y = \frac{9}{x ^{2} + 5 x + 6}

Replace

x

with

y

x = \frac{9}{y ^{2} + 5 y + 6}

Solve for

y, x = \frac{9}{y ^{2} + 5 y + 6}

\frac{- 5 x + x ^{2} + 36 x}{2 x}, \frac{- 5 x - x ^{2} + 36 x}{2 x}

\frac{3 x}{( x + 2 ) ^{2}}

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

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

\frac{x - 3}{x + 2}

f (x) = - x + 11

What is the inverse of f(x)= 9/((x^2+5x+6)) ?
The inverse of f(x)= 9/((x^2+5x+6)) is (-5x+sqrt(x^2+36x))/(2x),(-5x-sqrt(x^2+36x))/(2x)