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

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Answer 1 · 2015-12-03T01:07:50

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

Write as: $y=(2x+1)/x$

Swap $x$ and $y$ .

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

Solve for $y$ .

$xy=2y+1$

$xy-2y=1$

$y(x-2)=1$

$y=1/(x-2)$

You can rewrite $y$ as $f^-1(x)$ , which denotes an inverse function.

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

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