Answer
a) $7$
b) $10$
c) Limit does not exist.
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
a) Since, $ \lim_\limits{x\to 1^{-}} x=1$ when $ x \lt 1$
$\lim_\limits{x\to 1^{-}} x+6=1+6=7$
b) Since, $ \lim_\limits{x\to 1^{+}} x=1$ when $ x \gt 1$
$\lim_\limits{x\to 1^{+}} x+9=1+9=10$
c) From part (a) and (b) $\lim_\limits{x\to 1^{-}} \neq \lim_\limits{x\to 1^{+}}$
So, the limit does not exist.
