 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from katie, a student: Evaluate (if possible) the function of the given value of the independent variable: f(x)=(x^3)-x: [f(x)-f(1)]/(x-1) |
Hi Katie,
I'm going to illustrate using f(x) = x4 + x2 and evaluate [f(x)-f(2)]/(x-2).
f(x) - f(2)
= (x4 + x2) - (24 + 22)
= x4 - 24 + x2 - 22
= (x2 - 22)(x2 + 22) + (x - 2)(x + 2)
= (x - 2)(x + 2)(x2 + 22) + (x - 2)(x + 2)
= (x - 2)(x + 2)(x2 + 22 + 1)
= (x - 2)(x + 2)(x2 + 5)
Thus
[f(x)-f(2)]/(x-2)
= (x - 2)(x + 2)(x2 + 5)/(x - 2)
At this point you can cancel (x - 2) as long as x is not 2 so I would say
[f(x)-f(2)]/(x-2) = (x + 2)(x2 + 5) if x ≠ 2 and [f(x)-f(2)]/(x-2) is undefined if x = 2.
Penny
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.