For what value of the constant c
is the function
f
continuous on
(
−
∞
,
∞
)
where
f
(
b
)
=
{
c
b
+
9
if
b
≤
3
c
(
b
)
2
−
9
if
b
>
3

9514 1404 393

  c = 3

Step-by-step 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.

step-by-step explanation: