Find a value for the constant $c$ so that the function $$f(x)=\left\lbrace \begin{array}{ll} \frac{c}{x- 7} &\mbox{if}\ x< 5\\ 3 x-1 &\mbox{if}\ x\ge 5 \end{array}\right.$$ is continuous at $5$.
$c=$

Is $f$ then continuous at every real number?
Answer: Choose Yes No