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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
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
c
(c) $f:N \to I$

$f(1) = 0,\,f(2) = - 1,\,f(3) = 1,\,f(4) = - 2,\,f(5) = 2$

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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