SOLUTION: Im helping my son with his precalc. This problem is giving us problems. I have not been able to find similar problems on the web. It has to do with difference quotient. f(x) =

Algebra ->  Functions -> SOLUTION: Im helping my son with his precalc. This problem is giving us problems. I have not been able to find similar problems on the web. It has to do with difference quotient. f(x) =      Log On


   

Question 660213: Im helping my son with his precalc. This problem is giving us problems. I have not been able to find similar problems on the web. It has to do with difference quotient.
f(x) = 1/x
find (f(x)-f(1))/(x-1)
Thanks in advance,
Chris
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28f%28x%29-f%281%29%29%2F%28x-1%29

Let's start out working with the numerator f(x) - f(1)  only:

f(x) - f(1) = 1%2Fx - 1%2F1 = 1%2Fx - 1%2F1·x%2Fx = 1%2Fx - x%2Fx = %281-x%29%2Fx

Now let's divide that by the denominator x - 1:

%281-x%29%2Fx÷%28x-1%29 = %281-x%29%2Fx÷%28x-1%29%2F1 = %281-x%29%2Fx·1%2F%28x-1%29 

Now we have to play a trick with the 

1 - x

First arrange it in descending order

-x + 1

Factor out -1

-1(x - 1)

Now replace the 1 - x by that in  %281-x%29%2Fx·1%2F%28x-1%29 

%28-1%28x-1%29%29%2Fx·1%2F%28x-1%29

Cancel the (x - 1)'s

%28-1%28cross%28x-1%29%29%29%2Fx·1%2F%28cross%28x-1%29%29

-1%2Fx

Edwin