Question

Suppose f of x equals 3 times x minus k when x is less than 5 and equals 1 plus k times x when x is greater than or equal to 5.Find the value of k that would make f continuous at x = 5.


-3

0

7/3

no such k will make f continuous

Answer 1

suppose you use symbols instead of words:

f(x)
= 3x-k for x < 5
= kx+1 for x >= 5

for f to be continuous at x=5, we need

15-k = 5k+1
14 = 6k
k = 7/3