Question 63476
<pre><font face = "verdana" size = 5 color = "indigo"><b>Can you help me find the inverse of the
function g(x)= x/(x+2)

1. Replace g(x) by y

           y = x/(x+2)

2. Interchange x and y

           x = y/(y+2)

3. Solve for y:

           x = y/(y+2)

      x(y+2) = y

     xy + 2x = y

          2x = y - xy

          2x = y(1 - x)

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

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

4. Replace y by f<sup>-1</sup>(x)
      
      f<sup>-1</sup>(x) = (2x)/(1 - x)

To check, draw the graph of f(x)

{{{ graph( 300, 300, -5, 5, -5, 5,x/(x+2) ) }}}

On the same axis, draw the graph of f<sup>-1</sup>(x)

{{{ graph( 300, 300, -5, 5, -5, 5,x/(x+2), 2x/(1-x) ) }}}

Draw the indenty line, where y and x are identical, that
is, the line whose equation is y = x.

{{{ graph( 300, 300, -5, 5, -5, 5,x/(x+2), 2x/(1-x), x ) }}}

and we see that the original function and the inverse are
reflections of each other in the identity line, and form 
a symmetrical pattern. So the inverse is correct.

Edwin</pre>