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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = 5 x + 8

f (x) = \frac{x - 5}{10}

f (x) = \frac{3}{5} x - 4

3 x + 3

f (x) = \frac{2 x - 3}{x + 5}

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