Question

F(x) = 2x+1/×-1 find the inverse function

Answer 1

To factor this, start by replacing x with y and then solve for y
$f(x) = \frac{2x+1}{x - 1}$
$x = \frac{2y+1}{y - 1}$
$(y-1)x = \frac{2y+1}{y - 1} * (y-1)$
$(y-1)x = 2y+1$
$xy -x = 2y+1$
$xy - 2y -x +x = 2y - 2y +x+1$
$xy - 2y = x+1$
Factor out y on the left side. 
$\frac{xy - 2y}{y} = x+1$
$y(x - 2) = x+1$
$\frac{y(x - 2)}{(x-2)} = \frac{x+1}{x-2}$
$y = \frac{x+1}{x-2}$
$f(x)^{-1} = \frac{x+1}{x-2}$