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

The inverse of f(x)=(1-2x)/(4x(x-1)) is (2x-1+sqrt(4x^2+1))/(4x),(2x-1-sqrt(4x^2+1))/(4x)

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

inverse

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

\frac{2 x - 1 + 4 x ^{2} + 1}{4 x}, \frac{2 x - 1 - 4 x ^{2} + 1}{4 x}

Solution steps

y = \frac{1 - 2 x}{4 x ( x - 1 )}

Replace

x

with

y

x = \frac{1 - 2 y}{4 y ( y - 1 )}

Solve for

y, x = \frac{1 - 2 y}{4 y ( y - 1 )}

\frac{2 x - 1 + 4 x ^{2} + 1}{4 x}, \frac{2 x - 1 - 4 x ^{2} + 1}{4 x}

\frac{x ^{2}}{x + 7}

3. 2^{x}

- 2 x^{2} + 4

h (x) = e^{4 x + 1} - 2

\frac{- 4 x + 4}{- 2 x + 1}

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