What is the inverse of f(x)=(1-4x)/(2x+9) ?

The inverse of f(x)=(1-4x)/(2x+9) is (1-9x)/(2(2+x))

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inverse of f(x)=(1-4x)/(2x+9)

inverse

f (x) = \frac{1 - 4 x}{2 x + 9}

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

Solution steps

y = \frac{1 - 4 x}{2 x + 9}

Replace

x

with

y

x = \frac{1 - 4 y}{2 y + 9}

Solve for

y, x = \frac{1 - 4 y}{2 y + 9}

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

f (x) = 4 + 8 x - 5 x^{2}

f (x) = x + 9 - 2

f (x) = 2 x + 30

f (x) = - 3

x + 5

What is the inverse of f(x)=(1-4x)/(2x+9) ?
The inverse of f(x)=(1-4x)/(2x+9) is (1-9x)/(2(2+x))