What is the inverse of f(x)=(x+9)/(7-4x) ?

The inverse of f(x)=(x+9)/(7-4x) is -(9-7x)/(1+4x)

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inverse of f(x)=(x+9)/(7-4x)

inverse

f (x) = \frac{x + 9}{7 - 4 x}

- \frac{9 - 7 x}{1 + 4 x}

Solution steps

y = \frac{x + 9}{7 - 4 x}

Replace

x

with

y

x = \frac{y + 9}{7 - 4 y}

Solve for

y, x = \frac{y + 9}{7 - 4 y}

- \frac{9 - 7 x}{1 + 4 x}

f (x) = \frac{1}{5 x - 20}

\frac{4 x}{7 x - 1}

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

y = 7 x - 8

What is the inverse of f(x)=(x+9)/(7-4x) ?
The inverse of f(x)=(x+9)/(7-4x) is -(9-7x)/(1+4x)