or what value of the constant c is the function f continuous on (−∞,∞) where

Question

f(x)={cx+7cx2−7 if x∈(−∞,3] if x∈(3,∞)

Answer 1

any polynomial is continuous on any interval.

Looks like you are missing part of the function definition. As long as f(3) is the same for both parts, you're in.

So, look up the missing part of the definition and solve the equation for
f(3) = lim f->3+ f(x) on the right.