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

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

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

inverse

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

\frac{x}{x - 1}, - \frac{x}{x - 1}

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{x}{x - 1}, - \frac{x}{x - 1}

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