Answer
$2$
Work Step by Step
In exercise 6, we found that $\displaystyle \lim_{x\rightarrow 1}f(x)=2.$
Also, $f(1)=1$.
The function value at x=1 is different than the limit at x=1.
Apply the Continuity Test (see p.95),
1. $f(c)$ exists ( $c$ lies in the domain of $f$).
2. $\displaystyle \lim_{x\rightarrow c}f(x)$ exists ( $f$ has a limit as $x\rightarrow c$).
3. $\displaystyle \lim_{x\rightarrow c}f(x)=f(c)$ (the limit equals the function value).
Condition 3 is not satisfied, while the first two are.
If we changed the value of f(1) to 2,
then all three conditions of the Continuity Test would be satisfied, and f would be continuous at x=1.
