Question

For what value of the constant c is the function f continuous on (−∞,∞)
where f(s)={s 2 −c if s∈(−∞,8)
cs+1 if s∈[8,∞)

Answer 1

We want \[
\lim_{s\to 8^-}f(8) = \lim_{s\to 8^+}f(8)
\]Or\[
(8) ^2 −c=c(8)+1
\]

Answer 2

Now just solve for \(c\).