Browse Questions

# 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.

Toolbox:
• 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 $f(-1) and f(1)$

$f(-1)=(-1)^2=1\qquad f(1)=1^2=1$

$f(-1)=f(1)$

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