What is the inverse of f(x)=-sqrt((x-2)/(2x-6)) ?

The inverse of f(x)=-sqrt((x-2)/(2x-6)) is (-2+6x^2)/(2x^2-1)

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inverse of f(x)=-sqrt((x-2)/(2x-6))

inverse

f (x) = - \frac{x - 2}{2 x - 6}

\frac{- 2 + 6 x ^{2}}{2 x ^{2} - 1}

Solution steps

y = - \frac{x - 2}{2 x - 6}

Replace

x

with

y

x = - \frac{y - 2}{2 y - 6}

Solve for

y, x = - \frac{y - 2}{2 y - 6}

\frac{- 2 + 6 x ^{2}}{2 x ^{2} - 1}

f (x) = 3 + 2 x - 5

\frac{( x + 3 )}{x + 11}

f (x) = 11.25 x + 90

f (x) = \frac{4 x - 6}{2}

f (x) = 3 + 2 x - 4

What is the inverse of f(x)=-sqrt((x-2)/(2x-6)) ?
The inverse of f(x)=-sqrt((x-2)/(2x-6)) is (-2+6x^2)/(2x^2-1)