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  4. If the function f:R→ R denned by f(x)=[x] where [x] is the greatest integer not exceeding x, for x∈ R then f is

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Q. If the function $ f:R\to R $ denned by $ f(x)=[x] $ where $ [x] $ is the greatest integer not exceeding x, for $ x\in R $ then $f$ is

J & K CETJ & K CET 2007Relations and Functions

Solution:

We know that, a function is said to be even, if
$ f(-x)=f(x) $ and odd, if $ f(-x)=-f(x) $ and $ f(x) $
is increasing, if $ f'(x)>0 $
Here, $ f(x) $ is not differentiable at
$ x\in I $ and above two cases are also not satisfied by $ f(x) $
$ \therefore $ $ f(x)=[x] $ is neither even nor odd.