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If $$f(x)=\frac{x^{2}-x}{x-1} \quad \text { and } \quad g(x)=x$$is it true that f=g?
$f(x) \neq g(x)$
Calculus 1 / AB
Chapter 1
FUNCTIONS AND LIMITS
Section 1
Functions and Their Representations
Functions
Limits
Continuous Functions
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and this problem, we need to decide whether or not F of X is equal to G of X. We can do this by simplifying Methanex. You see there's a common factor. X in the numerator, said X Times X minus one over X minus one. We could simplify that f of X is equal to X now this makes it seem that f of X is equal to G of X. But that is not the case because we have to go back to F of X and notice that the domain of F of X is going to be different because of the denominator. So X minus one cannot equal zero because it will make ffx under find. So that means X cannot equal one. Now the graph of F of X is going to look like this. And since X cannot equal one, there is going to be a hole in the line. Well, the domain of G of X is X can be anything from night of infinity to infinity and its graph is going to look like this. Now we see that these two graphs are different because there is no hole in G of X Well, there is a hole in f of X due to having the possibility of being undefined. So this means that G of X and ethics are different, so they're not equal.
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