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:
Answer & explanation
Correct answer: option 3
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 $6.5$