Discuss the continuity if $f (x) = [x] + [- x]$ at integral points .

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Solution

Given: $f (x) = [x] + [- x]$
Greatest Integer function gives integer if the value is in decimal or integer
For example $[2.34] = 2$
The curve for G.I.F is shown below in which there is no continuous curve.
So G.I.F is discontinuous at every integer.

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