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Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 8 sub question (i) maths textbook solution.

Answers (1)

f is not bijective.


f:A \rightarrow A, given byf(x)=\frac{x}{2}

To prove:

Here we have to show that the given function is one-one and onto.


For one-one:

Let x_1 and x_2 be any two elements in the domain A, such that

\begin{aligned} & f\left(x_{1}\right)=f\left(x_{2}\right) \\ \Rightarrow & \frac{x_{1}}{2}=\frac{x_{2}}{2} \\ \Rightarrow & x_{1}=x_{2} \end{aligned}

So,f is one-one.

For onto:

Let y be any element in the codomain A, such that f(x)=(y) for some element x in domain A

Then,     f(x)=(y)

\Rightarrow \frac{x}{2}=y                                                                             \left [ f(x)=\frac{x}{2} \right ]

\Rightarrow x=2y, which may not be in A=[-1, 1]

So f is not onto.

Hence,f is not bijective.

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