Explain solution RD Sharma class 12 chapter Functions exercise 2.1 question 5 sub question (vi) maths
Neither injective nor surjective.
defined by .
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.
Bijective ⇒ Function should fulfill the injective, surjective condition.
Let us check if the given function is an injective, surjective, bijective.
Let x,y be any two elements in domain .
Here we cannot say that x=y.
Therefore, we have two number 2 and -3 in the domain z whose image is same as 6.
So f is not an injective.
Let y be any element in co-domain (R) such that for some element x in (R)
Here we can’t say .
So, f is not surjective and f is not a bijective.