What is the inverse of f(x)=sqrt((x-2)/(3-x)) ?

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

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inverse of f(x)=sqrt((x-2)/(3-x))

inverse

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

- \frac{- 2 - 3 x ^{2}}{x ^{2} + 1}

Solution steps

y = \frac{x - 2}{3 - x}

Replace

x

with

y

x = \frac{y - 2}{3 - y}

Solve for

y, x = \frac{y - 2}{3 - y}

- \frac{- 2 - 3 x ^{2}}{x ^{2} + 1}

f (x) = \frac{- 3 x - 2}{2 x - 1}

y = \frac{3 x + 2}{2 x - 5}

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

\frac{3 x ^{2} + 9 x - 12}{x ^{2} + 13 x + 36}

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

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