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  • Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (xi)

Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (xi)

Answers (1)

Neither injective nor surjective.

Given:

f:R \rightarrow R defined by f(x)=\sin ^{2}x+\cos ^2x.

Hint:

Injective (one-one): function means every element in the domain has a distinct image in the  co-domain.

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

Solution:

Injection condition:

f(x)=\sin ^{2}x+\cos ^2x

\sin ^{2}x+\cos ^2x=1 ( by formula)

So,f(x)=1 for every x in  R.

For all elements in the domain the image is 1. So,f is not an injective.

Surjection:

            Range of f=\left \{ 1 \right \}, 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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