What is the inverse of f(x)=(x+9)/(1-2x) ?

The inverse of f(x)=(x+9)/(1-2x) is -(9-x)/(1+2x)

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inverse of f(x)=(x+9)/(1-2x)

inverse

f (x) = \frac{x + 9}{1 - 2 x}

- \frac{9 - x}{1 + 2 x}

Solution steps

y = \frac{x + 9}{1 - 2 x}

Replace

x

with

y

x = \frac{y + 9}{1 - 2 y}

Solve for

y, x = \frac{y + 9}{1 - 2 y}

- \frac{9 - x}{1 + 2 x}

y = - x - 6

y = x^{2} + 6 x + 5

y = - x - 5

f (x) = 2 (x + 5)^{2} - 6

- x^{2} - 2

What is the inverse of f(x)=(x+9)/(1-2x) ?
The inverse of f(x)=(x+9)/(1-2x) is -(9-x)/(1+2x)