Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (v)
Neither an injection nor a surjection.
, defined by .
Injective function means every element in the domain has a distinct image in the co-domain.
function means every element in the co-domain has at least one pre image in the domain of function.
Bijection ⇒ Function should fulfill the injection, surjection condition.
Let us check if the given function is injective, surjective, or bijective.
Let x and y be any two elements in the domain (R) such that
Therefore f is not an injection.
Let y be any element in the codomain (R) , such that for some element x in R .
Therefore, f is surjective.
Since f is not an injective , but surjective. So the f is not bijective.