Question

Find the value of the constant b that makes the following function continuous on (-\infty,\infty).
f(x) = 4x-5 if x < or = to 5
f(x) = -8x+b if x > 5

Answer 1

The two functions will be continuous if they have the same value at x = 5, where the two functions switch off. So at x = 5, the first function:
f(x) = 4x-5
f(5) = 4(5) - 5 = 15

So what you need to do is plug in 5 into the other function and find the value of b that will make the answer equal to 15.

Answer 2

Okay, so 55 would be the answer. Thanks

Answer 3

Yep :)