# Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(iv)\quad k(x)\;=\;x^2$

Note: This is the 4th part of a  4 part question, which is split as 4 separate questions here.

Toolbox:
• 1.A function f on set A is one-one if $f(x)=f(y) =>x,y \in A$
• 2.A function f on set A is onto if for every $y \in A$ then exists $x \in A$ such that $f(x)=y$
• 3.A function is bijective if it is both one-one and onto
$k(x)=x^2 \qquad [-1,1]$

Let $k(x_1)=x(x_2)=1 \qquad x_1x_2 \in [-1,1]$

$k(-1)=(-1)^2=1$

$k(1)=(1)^2=1$

Therefore $k(x_1)=k(x_2)$

does not imply $x_1=x_2$

Hence k is not one one

Let $y=-1$ then there is no element $x \in [-1,1]$ such that $k(x)=x^2=-1$

Hence k is not onto.

Hence k is neither one-one nor onto