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Question:

If f(x) = [x] - [x/4], x ∈ R, where [x] denotes the greatest integer function, then:

Both limx→4-f(x) and limx→4+f(x) exist but are not equal

f is continuous at x=4

limx→4-f(x) exists but limx→4+f(x) does not exist

limx→4+f(x) exists but limx→4-f(x) does not exist

Solution:

The correct option is B
f is continuous at x=4
limx→4+f(x) = limx→4+(([x] - [x/4])) = 4 - 1 = 3
limx→4-f(x) = limx→4-(([x] - [x/4])) = 3 - 0 = 3
f(x) = 3
∴ continuous at x=4