Find the values of a so that the function is continuous at x = 2.

Given:

The function f is continuous at x = 2

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.

⇒ 2a + 5

since f is continuous at x = 2,

∴ 2a + 5 = 1

⇒ 2a = 1 – 5

⇒ 2a = –4

⇒ a = –2

Thus, f is continuous at x = 2 if a = –2.