more calculus?

Question

For what value of the constant c is the function of f continuous on (-infinity,infinity) where
1.
f(s) = cs+2 if s E (-INF, 9]
cs^2-2 if s E (9, INF)
c=??

2.
f(t) = t^2-c if t E (-INF, 3)
ct+2 if t E [3, INF)
c=??

Answer 1

To be continuous the two functions have to have the same value at s = 9. So:

cs+2 = cs^2-2
cs^2 - cs - 4 = 0
81c - 9c - 4 = 0
c = 4/72 = 1/18

2. Must be the same at t = 3

t^2 - c = ct+2
t^2 - c - ct - 2 = 0
9 - c - 3c - 2 = 0
c = 7/4