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Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 8 sub question (iii)

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f is not bijective.


            h:A\rightarrow A, given byh(x)=(x)^2

To prove:

Function h is one-one, onto or bijective.


For any function to be bijective, the given function should be one-one and onto.


First we will check whether the given function is one-one or not.

We know for function h to be one-one

\begin{aligned} &\begin{aligned} & h\left(x_{1}\right)=h\left(x_{2}\right) \\ \Rightarrow & x_{1}^{2}=x_{2}^{2} \\ \Rightarrow & x_{1}=\pm x_{2} \end{aligned}\\ &\text { So, } h \text { is not one-one. } \end{aligned}


Let h(x)=y such thaty \in A


Hence, the value of y is defined only if y is positive,

But y is a real number

Hence, if y is negative, there is not corresponding element of x

i.e; for y=-1 , there is no value of x in A. 

Hence, h is not onto.

Hence, h is not bijective.

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