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

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f is not bijective


g:A \rightarrow A, given byg(x)=\left | x \right |

To prove:

Function f is one-one, onto or bijective.


For any function to be a 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 one-one function

\begin{aligned} &\Rightarrow \quad g\left(x_{1}\right)=g\left(x_{2}\right) \\ &\Rightarrow \quad\left|x_{1}\right|=\left|x_{2}\right| \\ &\Rightarrow \quad x_{1}=\pm x_{2} \end{aligned}

So, g is not one-one.

g(x)=\left | x \right |

Let g(x)=ysuch 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;  y=-x, there is no value of x inA    

Hence, f is not onto.

So, g is not onto.

Hence g is not bijective.

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