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

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

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

inverse

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

\frac{1 + - x ( - x + 1 ) + 1}{x}, \frac{1 - - x ( - x + 1 ) + 1}{x}

Solution steps

y = \frac{2 x - 1}{x ^{2} - 1}

Replace

x

with

y

x = \frac{2 y - 1}{y ^{2} - 1}

Solve for

y, x = \frac{2 y - 1}{y ^{2} - 1}

\frac{1 + - x ( - x + 1 ) + 1}{x}, \frac{1 - - x ( - x + 1 ) + 1}{x}

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