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Give an example of a map$(ii)\quad which\;is\;not\;one-one\;but\; not\; onto$

Note: This is the 2nd part of a  3 part question, which is split as 3 separate questions here.

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  • 1. function $:A \to B$ is one-one if $f(x)=f(y) =>x=y\qquad x,y \in A$
  • 2.A function $f:A \to B$ into if for every $y \in B$ then exists $ x \in $ such that $f(x)=y$
(ii) Let $ f:R \to R_+$ given by $f(x)=x^2$
consider $f(-1) and f(1)$
$f(-1)=(-1)^2=1\qquad f(1)=1^2=1$
but $-1=1$
Hence f is not one-one
For every element $ y \in R_+$ then exists an element $f(x)=y\qquad y \in R_+$
Hence f is not one-one but onto



answered Mar 4, 2013 by meena.p

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