A function f(x) = x^2-x/x-1 for all x except x = 1. For the function to be continuous at x=1, the value of f(1) must be ___? The answer was 2, but I don't know how to prove this. Help please!

Question

.sam. · Answer

f(x) = x^2-x/x-1 is a straight line and so it is continuous for $-\infty ~to~ +\infty$, With the exception for x=1 bcause when x=1, the denominator will be zero which is not valid

anonymous · Answer

Yes, I know the function would be undefined at x = 1. But why must the function equal 2 at x =1 instead of any other number?

.sam. · Answer

Are you sure its 2...
$$\large \lim_{x \rightarrow 1} \frac{x^2-x}{x-1} \ \ \large  \lim_{x \rightarrow 1} \frac{x\cancel{(x-1)}}{\cancel{x-1}} \ \ \large  \lim_{x \rightarrow 1}~x \ \ =1$$

anonymous · Answer

Yeah, when I first tried to solve for it, I thought it would be 1 too. This is a question from Barron's AP Calc (I don't know which version), but the answer key says it is 2.