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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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