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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

y = 16 x^{2} - 24 x + 9

(- 4, 0), (5, 9)

x^{2} - 8 x + 15

f (x) = - x^{2} + 5 x - 4

(- 5.9) (8.14)

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