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

Question

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

f(s)= {cs+6 if s∈(−∞,7)

= { cs^2−6 if s∈(7,∞)

Answer 1

Set s = 7 for each function rule in the piecewise definition and set those expressions = to each other:

7c + 6 = 49c - 6

c = 2/7