What is the inverse of f(x)=(3x+6)/(x^2+9) ?

The inverse of f(x)=(3x+6)/(x^2+9) is (3+sqrt(9-4x(9x-6)))/(2x),(3-sqrt(9-4x(9x-6)))/(2x)

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inverse of f(x)=(3x+6)/(x^2+9)

inverse

f (x) = \frac{3 x + 6}{x ^{2} + 9}

\frac{3 + 9 - 4 x ( 9 x - 6 )}{2 x}, \frac{3 - 9 - 4 x ( 9 x - 6 )}{2 x}

Solution steps

y = \frac{3 x + 6}{x ^{2} + 9}

Replace

x

with

y

x = \frac{3 y + 6}{y ^{2} + 9}

Solve for

y, x = \frac{3 y + 6}{y ^{2} + 9}

\frac{3 + 9 - 4 x ( 9 x - 6 )}{2 x}, \frac{3 - 9 - 4 x ( 9 x - 6 )}{2 x}

r an g e 9 + x

cr i t i c a l f (x) = x e^{- x^{2}}

l in e (12, 0), (0, 6)

in v erse f (x) = x^{\frac{- 1}{4}}

r an g e f (x) = ln (5 - x)

What is the inverse of f(x)=(3x+6)/(x^2+9) ?
The inverse of f(x)=(3x+6)/(x^2+9) is (3+sqrt(9-4x(9x-6)))/(2x),(3-sqrt(9-4x(9x-6)))/(2x)