Expert: Paul Klarreich - 10/2/2008

Question
can you evaluate the function f(x)=x^3 + x at the independent variable
f(x)-f(1)/x-1


Answer
Questioner:   Martin
Category:  Advanced Math
Private:  No
 
Subject:  functions
Question:  can you evaluate the function f(x)=x^3 + x at the independent variable
f(x)-f(1)/x-1
...........................
Hi, Martin,

Are you sure you typed the question correctly?  This is what you have asked:

To compute

f( (f(x) - f(1)) / (x-1)) = ( f(x)-f(1))/(x-1) )^3 + ( f(x)-f(1))/(x-1) )

But I think you meant to write:

If  f(x) = x^3 + x, compute and simplify the difference quotient:

f(x) - f(1)    x^3 + x - (1 + 1)
------------ = ------------------ =
 x - 1            x - 1

x^3 + x - 2     (x - 1)(x^2 + 2)
------------- = ---------------- = x^2 + 2
   x - 1           x - 1

Next time, please READ MY INSTRUCTIONS, which include the request that you:

(5) Include the WHOLE question, with the instructions.

-- exactly as you see it in the book.