Question 74104
{{{f(x)=(x-1)/(x+1)}}}If thats what f(x) looks like then we're going to add that to f(1/x). 
To find f(1/x) we simply plug in (1/x) in for every x in the original equation.
{{{f(1/x)=(highlight(1/x)-1)/(highlight(1/x)+1)}}}
{{{f(1/x)=((1/x)-(x/x))/((1/x)+(x/x))}}}
{{{f(1/x)=((1-x)/x)/((1+x)/x)}}}
{{{f(1/x)=((1-x)/cross(x))*(cross(x)/(1+x))}}}
So f(1/x) equals
{{{f(1/x)=((1-x)/(1+x))}}}
Add this to f(x)
{{{f(x)+f(1/x)=(x-1)/(x+1)+((1-x)/(1+x))}}}
{{{f(x)+f(1/x)=(x-x+1-1)/(x+1)}}}
{{{f(x)+f(1/x)=(0)/(x+1)}}}
{{{f(x)+f(1/x)=0}}}
So for any x 
{{{f(x)+f(1/x)=0}}}
<p>
Check:
We can let x equal any number. Lets make x=2
{{{f(x)=(x-1)/(x+1)}}}Plug in x=2
{{{f(2)=(2-1)/(2+1)=1/3}}}
{{{f(1/x)=((1-x)/(1+x))}}}Plug in x=2
{{{f(1/2)=(1-2)/(1+2)}}}
{{{f(1/2)=-1/3}}}
{{{f(x)+f(1/x)=f(2)+f(1/2)=1/3-1/3=0}}}Add the two equations. This shows that our answer works.