How do I explain this?

Let f(x) be a real function and 𝑥 ∈ ℝ. Assume that lim𝑥→𝑎 𝑓(𝑥) = 𝑙, where 𝑎, 𝑙 ∈ ℝ.

 

Is this sufficient to conclude that 𝑓(𝑎) = 𝑙 (and hence the continuity of f(x) at 𝑎)? Provide a detailed explanation and, if necessary, discuss discontinuity