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

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

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inverse of f(x)=sqrt((3x-1)/(2x-1))

inverse

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

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

Solution steps

y = \frac{3 x - 1}{2 x - 1}

Replace

x

with

y

x = \frac{3 y - 1}{2 y - 1}

Solve for

y, x = \frac{3 y - 1}{2 y - 1}

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

(x - 6) (x - 8)

f (x) = \frac{4 x - 2}{x + 7}

\frac{- x + 1}{5 + 7 x}

1 - e^{- y}

f (x) = 3 - 12 x

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