Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (x)
Surjective but not injective
, defined by
Injective function means every element in the domain has a distinct image in the co-domain.
surjective function means every element in the co-domain has at least one pre image in the domain of function.
Let x and y be any two elements in the domain (R), such that
Here we cannot say
So, -1 and 1 have the same image 0.
Thus f is not an injection.
Let x and y be any two elements in the domain (R) such that for some element (R) in R.
In order to identity surjection,
Therefore, f is a surjective.
Therefore, f is not a bijective.