A function f from the set of natural numbers to integers defined … - Vidyadip

MCQ

A function $f$ from the set of natural numbers to integers defined by $f(n) = \left\{ \begin{array}{l}\frac{{n - 1}}{2},\;{\rm{when}}\;n\;{\rm{is}}\;{\rm{odd}}\\ - \frac{n}{2},\;{\rm{when\, }}n{\rm{\, is\, even}}\end{array} \right.$, is

A
One$-$one but not onto
B
Onto but not one$-$one
✓
One$-$one and onto both
D
Neither one$-$one nor onto

✓

Answer

Correct option: C.

One$-$one and onto both

$f:N \to I$$f(1) = 0,\,f(2) = - 1,\,f(3) = 1,\,f(4) = - 2,\,f(5) = 2$
and $f(6) = - 3$ so on.
In this type of function every element of set $A$ has unique image in set $B$ and there is no element left in set $B$.
Hence $f$ is one$-$one and onto function.

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