For what value of the constant c is the function f continuous on (-infinity, inf.) where f(a)=(ca+5 if a?

(-inf,6] or ca^2-5 if a (6,inf)

For what value of the constant c is the function f continuous on (-infinity, inf.) where f(a)=(ca+5 if a?
obviously the function is continuous everywhere except at a=6, no matter what c is. So compute the two values at 6 (which technically are the left and right limits of the function at 6.)


get 6c+5 (left) and 36c-5 (right)


equate


6c+5 = 36c-5


30c=10


c=1/3

kudzu