Question

For what value of the constant c is the function f continuous on

(−∞,∞) where

f(b) = { cb + 9 if b ≤ 3
c(b)² − 9 if b > 3

Answer 1

9514 1404 393

Answer:

c = 3

Explanation:

In order for the function to be continuous at b=3, the left and right limits must be the same. In short, we must have ...

c(3) +9 = c(3²) -9

18 = 6c . . . . . . . . add 9-3c to both sides

3 = c . . . . . . . . . . divide by 6

Function f is continuous when c=3.