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Question
Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.
Solution
We have, f(x) = x — [x]
Injection test:
f(x) = 0 for all x ∈ Z
So, f is a many-one function.
Surjection test:
Range (f) = [0, 1) ≠ R.
So, f is an into function.
Therefore, f is neither one-one nor onto.
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