Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 19: 2

$f$ is not equal to $g$

We rewrite the function $f$: $$f(x)=\frac{x^2-x}{x-1}=\frac{x(x-1)}{x-1}=x,\text{ where }x\not=1.$$ So for $x\not=1$ we have $f(x)=g(x)=x$. Even though the two functions seem equal, they are not equal because $f$ is not defined for $x=1$, while $g$ is. Therefore, because the two functions do not have the same domain, $f$ is not equal to $g$.