If f(x) = (x^2 - x)/(x - 1) and g(x) = x, s it true that f = g?

Expert Answers
justaguide eNotes educator| Certified Educator

The function `f(x) = (x^2 - x)/(x - 1)` and g(x) = x.

It is possible to write f(x) as:

`f(x) = (x^2 - x)/(x - 1)`

= `(x*(x - 1))/(x - 1)`

Now the common factor x - 1 can be eliminated to give:

f(x) = x

But note that in the original function `f(x) = (x^2 - x)/(x - 1)` , if x = 1, the value of f(x) is not defined as it takes the form `0/0` . On the other hand g(x) = x has the value 1 at x = 1.

The two functions are not equivalent for all values of x. It would be possible to say that f = g if g(x) is defined as `g(x) = x` , `x!= 1` .