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

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Answer 1 · 2015-12-13T00:35:37

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

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

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

Switch $x$ for $y$ and $y$ for $x$

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

Multiply both side by $y+2$

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

Distribute

$xy+2x = y-2$

Bring all "y" term to one side and factor

$2x+2 = y-xy$

Factor, and solve for $y$

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

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

Replace $y$ with inverse notation $f^(-1)(x)$

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

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