For what value of is the function defined below continuous on ?

Question

For what value of  is the function defined below continuous on ?

Answer 1

The piecewise function will be continuous at the value(s) of c

that give the the same value for the two pieces of the function f(x):

x² – c² = cx +80, when x = 8

In other words, the value of c where (8)² – c² = c(8) + 80 is our solution,

which means that

64 – c² = 8c + 80

Adding c² – 64 to both sides gives

0 = 8c + 80 + c² – 64 = c² + 8c +16 = (c + 4)²

answer

f(x) is continuous on (–∞,∞) when c = –4