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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
A function f from the set of natural numbers to integers defined by $f(n)=\left\{\begin{array}{l}\frac{n-1}{2}, \text { when } n \text { is odd } \\ -\frac{n}{2}, \text { when } n \text { is even }\end{array}\right.$, is
  • A
    One-one but not onto
  • B
    Onto but not one-one
  • C
    One-one and onto both
  • D
    Neither one-one nor onto
✓

Answer

(C)
$f : N \rightarrow I$
$\begin{array}{l}f(1)-0, f(2)=-1, f(3)=1, f(4)=-2, f(5)=2 \\ \text {and } f(6)=-3 \text { so on. }\end{array}$
Image
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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