Need solution for RD Sharma maths class 12 chapter Functions exercise 2.1 question 5 sub question (i)
One-one but not onto.
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's start with the injection test.
Let x and y be any two elements in the domain(N) such that
Where x and y are in N , so we don’t get 1 value.
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
If which is not in N .
So,f is not a surjection.
The condition of bijection is as we know the function should be one-one and onto.
Hence for this, f is not bijection.