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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = 3 + cos (x)

f (x) = 5^{2 x - 1} + 2

f (x) = x^{2} - 13, x \geq 0

f (x) = 5 + 3 a x

f (x) = 2^{x - 2}

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