The function $f(x) = [x]$, where [x] denotes the greatest integer function, is continuous at x =

(A) 2.9
(B) 5
(C) -3
(D) 6.5

Choose the correct answer from the options given below:

(A) and (D) only

The correct answer is Option (3) → (A) and (D) only

$f(x)=[x]$ is discontinuous at every integer and continuous at every non-integer.

Check the options:

(A) $2.9$ is not an integer → continuous.

(B) $5$ is an integer → discontinuous.

(C) $-3$ is an integer → discontinuous.

(D) $6.5$ is not an integer → continuous.

Final answer: $2.9$ and $6.5$