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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 6 + 2 x - 4

y = x^{2} + 8 x

f (x) = \frac{1}{5} x - 5

f (x) = 10239 e - 9.304

tan (\frac{π}{4})

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