$(15$ points$)$

Consider

$f(x)=\{\begin{array}{cc}{e}^{x^2-9}-a,& x<mn>3</mn>\\ b,& x=3\\ \frac{3}{x}-1\\ x-3,& x>3\end{array}$

where a and $b$ are constants $($parameter$).$ Is it possible to choose a value for a and $b$ such that $f(x)$ is continuous at $x=3?$ Explain your reasoning completely and justify with limit computations.