SOLUTION: can you help me to explain this equation? If f(x)=x-1/x+1 then f(x)+f(1/x)= this is a homework assignment..but not in our book..thanks

Question 74104: can you help me to explain this equation?
If f(x)=x-1/x+1 then f(x)+f(1/x)=
this is a homework assignment..but not in our book..thanks
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If f(x)= x-1/x+1 then f(x)+ f(1/x) =
:
Deal with f(1/x) first, substitute (1/x) for x in f(x) = x - (1/x) + 1:
:
f(1/x) = (1/x) - 1/(1/x) + 1
:
1/(1/x) is equal to x so you have:
f(1/x) = (1/x) - x + 1
:
It wants f(x) + f(1/x); we just found f(1/x) and f(x) was given originally
so we have
(x - (1/x) + 1) + ((1/x) - x + 1) =
:
Combine like terms
x - x - (1/x) + (1/x) + 1 + 1 = 2 is the solution
:
Did this help?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.

So f(1/x) equals

Add this to f(x)

So for any x

Check:
We can let x equal any number. Lets make x=2
Plug in x=2

Plug in x=2

Add the two equations. This shows that our answer works.
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