Find value where f(x) is continuous everywhere

Question

To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

 

Question options:

1)	1.88
2)	9.00
3)	3.76
4)	None of these

Answer 1

for a function to be continuous the limit as the point is approached from the left has to be equal to that when approached from the right. Thus 3x+k=kx^2-6 when x=3 yielding k= 15/8 = 1.88