What is the inverse of f(x)=(x^2)/(x^2-9) ?

The inverse of f(x)=(x^2)/(x^2-9) is (3sqrt(x)sqrt(x-1))/(x-1),-(3sqrt(x)sqrt(x-1))/(x-1)

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inverse of f(x)=(x^2)/(x^2-9)

inverse

f (x) = \frac{x ^{2}}{x ^{2} - 9}

\frac{3 x x - 1}{x - 1}, - \frac{3 x x - 1}{x - 1}

Solution steps

y = \frac{x ^{2}}{x ^{2} - 9}

Replace

x

with

y

x = \frac{y ^{2}}{y ^{2} - 9}

Solve for

y, x = \frac{y ^{2}}{y ^{2} - 9}

\frac{3 x x - 1}{x - 1}, - \frac{3 x x - 1}{x - 1}

What is the inverse of f(x)=(x^2)/(x^2-9) ?
The inverse of f(x)=(x^2)/(x^2-9) is (3sqrt(x)sqrt(x-1))/(x-1),-(3sqrt(x)sqrt(x-1))/(x-1)