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

Note: This is the 2nd 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 ie $f(x)=f(y)=>x=y \qquad x,y \in A$
• 2.A function f on set A is onto if for every $y \in A$ than exist $x\in A$ such that $f(x)=y$
• 3.A function is bijective if it is both one-one and onto
(ii)$g(x)=|x| \qquad a \in [-1,1]$

Let $x_1=-1\;and \; x_2=1$

$g(x_1)=|-1|=g(x_2)|1|=1$

but $x_1 \neq x_2$

Hence g is not a one one function

Consider y=-1 we cannot find any no. $x \in A$ such that $g(x)=y=-1$

modulus of a number is always positive

Therefore g is neither one -one nor onto