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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x-1%29%2F%28x%2B1%29If 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%281%2Fx%29=%28highlight%281%2Fx%29-1%29%2F%28highlight%281%2Fx%29%2B1%29
f%281%2Fx%29=%28%281%2Fx%29-%28x%2Fx%29%29%2F%28%281%2Fx%29%2B%28x%2Fx%29%29
f%281%2Fx%29=%28%281-x%29%2Fx%29%2F%28%281%2Bx%29%2Fx%29
f%281%2Fx%29=%28%281-x%29%2Fcross%28x%29%29%2A%28cross%28x%29%2F%281%2Bx%29%29
So f(1/x) equals
f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29
Add this to f(x)
f%28x%29%2Bf%281%2Fx%29=%28x-1%29%2F%28x%2B1%29%2B%28%281-x%29%2F%281%2Bx%29%29
f%28x%29%2Bf%281%2Fx%29=%28x-x%2B1-1%29%2F%28x%2B1%29
f%28x%29%2Bf%281%2Fx%29=%280%29%2F%28x%2B1%29
f%28x%29%2Bf%281%2Fx%29=0
So for any x
f%28x%29%2Bf%281%2Fx%29=0


Check:
We can let x equal any number. Lets make x=2
f%28x%29=%28x-1%29%2F%28x%2B1%29Plug in x=2
f%282%29=%282-1%29%2F%282%2B1%29=1%2F3
f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29Plug in x=2
f%281%2F2%29=%281-2%29%2F%281%2B2%29
f%281%2F2%29=-1%2F3
f%28x%29%2Bf%281%2Fx%29=f%282%29%2Bf%281%2F2%29=1%2F3-1%2F3=0Add the two equations. This shows that our answer works.