HELP PLEASE! :)

The answer is a = 5.

I am not sure how Guest arrived at a=5, but that answer is incorrect.

In order for a function to be continuous at x=c, the function must fulfill three criteria. They are the following:

     1) $f(c)$ is defined.

     2) $\lim_{x\rightarrow c}f(x)$ is defined.

     3) $\lim_{x\rightarrow c}f(x)=f(c)$

Right now, only one criterion is met currently. $f(3)$ is defined in this piecewise function because $x=3$ is included in the domain. Let's move on to the next condition.

In order for $\lim_{x\rightarrow c}f(x)$ to be defined, we have to ensure that left-side and right-side limit approach the same value. We set both limits equal to each other and find possible values for a, if one exists.

$\lim_{x\rightarrow 3^-}f(x)=\lim_{x\rightarrow 3^+}f(x)\\ 3*3^2+2=3a-1\\ 29=3a-1\\ 3a=30\\ a=10$

At $a=10$, both limits approach the same value. Therefore, we have met the second condition.

Finally, we have to make sure that the limit and the true value are not incongruous.

$\lim_{x\rightarrow 3}f(x)\stackrel{?}{=}f(3)\\ 29=29$

Yes, that means that a=10 makes the function continuous.