Fundamentholfundamenthol
JEE Main2019Math
Q.

Let N be the set of natural numbers and two functions f and g be defined as

f, g : N N such that

\,f\left( n \right)\, = \left\{ {\begin{array}{*{20}{c}} {\dfrac{{n + 1}}{2}\,\,\,\,\,if\,n\,{\text{is}}\,{\text{odd}}} \\ {\dfrac{n}{2}\,\,\,\,\,if\,n\,\,{\text{is}}\,{\text{even}}} \end{array}} \right.

and g(n) = n – (–1)n. Then fog is :

  1. A

    One-one but not onto

  2. B

    Onto but not one-one

  3. C

    Neither one-one nor onto

  4. D

    Both one-one and onto

Solution

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