How do you find the inverse of $f(x) = (2x-1)/(x-1)$ ?

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Answer 1 · 2015-11-21T18:40:19

Let $y = f(x)$ and solve for $x$ to find:

$f^(-1)(y) = (y-1)/(y-2)$

$y = f(x) = (2x-1)/(x-1) = (2x-2+1)/(x-1) = (2(x-1)+1)/(x-1)$

$= 2+1/(x-1)$

Subtract $2$ from both ends to get:

$y-2 = 1/(x-1)$

Hence:

$x-1 = 1/(y-2)$

Add $1$ to both sides to get:

$x = 1/(y-2)+1 = (1+(y-2))/(y-2) = (y-1)/(y-2)$

So $f^(-1)(y) = (y-1)/(y-2)$

How do you find the inverse of f(x) = (2x-1)/(x-1)f(x) = (2x-1)/(x-1)?