The given function f(x) will be continuous at x = 2, if

lim

x→2−

f (x) =

lim

x→2+

f (x) = f (2)

lim

x→2−

=

lim

x→2−

2x + 1 = 2 × 2 + 1 = 5

lim

x→2−

=

lim

x→2−

3x + 1 = 3 × 2 - 1 = - 5
∴ f (2) = k
⇒ k = 5
Thus, for k = 5, the given function is continuous at x = 2.