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

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

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inverse of f(x)=sqrt(2-x/(x-2))

inverse

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

\frac{2 x ^{2} - 4}{x ^{2} - 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{2 x ^{2} - 4}{x ^{2} - 1}

8 x^{2}

f (x) = x^{2} + 10

\frac{y}{y + 2}

x^{2} + 3 x - 4

x^{4} - x^{2}

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