Section 1.5 Prob 4

Question

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

f(x)={ cx+8 if x ∈(−∞,7]

cx^2-8 if x∈(7,∞)

Answer 1

If the function is to be continuous, the limits must match from both the left side and the right side at the point of contention (in this case x = 7 )

lim cx+8

x --> 7^-

lim cx² - 8

x --> 7⁺

Currently at the value of 7 we have f(x) = {7c + 8 , 49c - 8 }. We want these limits to be equal...

7c + 8 = 49c - 8

16 = 41c

c = 16/41