Question

For what value of the constant c is the function f continuous on ( -\infty , \infty ) where
f( t ) = \begin{cases} { t }^2 - c & \text{ if } t \in (-\infty, 2) \quad \quad \\ c { t } + 8 & \text{ if }t \in [ 2 , \infty) \quad \quad \end{cases}


c= ?

Answer 1

in order to make them continous they both need to be equal when the functions change.
so basically they need to be equal when t is 2

Answer 2

ok

Answer 3

and then i solve the equations?

Answer 4

okay so for the function to be continuous in all R, at t=2, the two different part of the function will have to be equal.
so, t^2-c=ct+8
put t=2, simplify and get value of c. then enjoy!!

Answer 5

\[4- c = 2c + 8\]

Answer 6

-4/3

Answer 7

thanks

Answer 8

correct!