It is given f : R → R, given by f (x) = [x]
We can see that f(1.2) = [1.2] = 1
f(1.9) = [1.9] = 1
⇒ f(1.2) = f(1.9), but 1.2 ≠ 1.9.
⇒ f is not one- one.
Now, let us consider 0.6 ϵ R.
We know that f(x) = [x] is always an integer.
⇒ there does not exist any element x ϵ R such that f(x) = 0.6
⇒ f is not onto.
Therefore, the greatest integer function is neither one-one nor onto.
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