Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (iii)
Injective but not surjective.
given 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.
For any function to be a bijective, the given function be one-one and onto.
Let us check for the given function is injection, surjection and bijection.
Let's start with the injection test.
Let x and y be any two elements in the domain (N) such that
So,f is an injection
Let y be any element in the codomain (N) , such that for some element x in N .
which may not be in N
So,f is not a surjection.
Here f is injective but not surjective, so the f is not a bijective.
The condition of bijection is as we know the function should be one-one and onto.
Hence for this, f is not bijection.