For what value of the constant c is the function f continuous on (-/infty, / infty) where

f (t) =

{t2-cct+8 if t∈ (-∞,2) if t∈[2,∞)

c = ?

The function is:

f (t) = t2-c if t∈ (-∞,2)

f (t) = ct+8 if t∈[2,∞)

Continuity means that there are not holes or jumps, so the limt of t^2 - c as t approachs to 2 by the left must be equal to the value of f (t) when t = 2

Limt (as t - > 2 by the left) of t^2 - c = 2^2 - c = 4 - c

and f (2) = c (2) + 8 = 2c + 8

=> 2c + 8 = 4 - c = > 3c = 4 - 8 = - 4

c = - 4/3

Answer: c = - 4/3