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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = \frac{x + 1}{x}

f (x) = \frac{2}{3} x - 6

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

f (x) = x - 1 - 2

f (x) = \frac{2 x}{x + 2}

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