What is the inverse of f(x)=(3x-2)/(5x+9) ?

The inverse of f(x)=(3x-2)/(5x+9) is (-2-9x)/(5x-3)

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inverse of f(x)=(3x-2)/(5x+9)

inverse

f (x) = \frac{3 x - 2}{5 x + 9}

\frac{- 2 - 9 x}{5 x - 3}

Solution steps

y = \frac{3 x - 2}{5 x + 9}

Replace

x

with

y

x = \frac{3 y - 2}{5 y + 9}

Solve for

y, x = \frac{3 y - 2}{5 y + 9}

\frac{- 2 - 9 x}{5 x - 3}

f (x) = \frac{- 7 + 5}{- 7 + 7}

\frac{1}{2 x - 5}

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

f (x) = 4 x^{11} + 7

f (x) = 15 - 5 y

What is the inverse of f(x)=(3x-2)/(5x+9) ?
The inverse of f(x)=(3x-2)/(5x+9) is (-2-9x)/(5x-3)