Determine the value of the constant k so that the function is continuous at x = 2.

Given:

It is clear that when x<2 and x>2, the given function is continuous at x = 2.

So, at x = 2

= 4k

We know that,

If f is continuous at x = c, then The Left–hand limit, the Right–hand limit and the value of the function at x = c exist and are equal to each other.

⇒ 4k = 3

k =

Therefore, the required value of k is