Q. 74.3( 3 Votes )
Discuss the continuity of f(x) = [x].
Answer :
Let n be any integer
[x] = Greatest integer less than or equal to x.
Some values of [x] for specific values of x
[3] = 3
[4.4] = 4
[-1.6] = -2
Therefore,
Left hand limit at x = n
= 
= n – 1
Right hand limit at x = n
= 
= n
Also, f(n) = [n] = n
As 
Therefore, f(x) = [x] is discontinuous at x = n.
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