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Explain solution RD Sharma class 12 chapter Functions exercise 2.1 question 5 sub question (viii) maths

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Neither injective nor surjective.


f:R \rightarrow R  defined by f(x)=\sin x.


One-one function means every element in the domain has a distinct image in the  co-domain.

Onto function means every element in the co-domain has at least one  pre image in the domain of function.


Injection test

Let x and y be any two elements in the domain (R) such thatf(x)=f(y)

\sin x=\sin y

Here x  may not be equal to y  because \sin 0 = \sin \pi =0 

So, f  is not an injection.

Surjection test:

Range of f=[-1,1]

Co-domain of f=R

Both are not the same.

So f  is not a surjection and f is not a bijection.

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