Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 1 sub question (i) maths textbook solution.
The example for a function which is one-one but not onto.
One-one function means every element in the domain has a distinct image in the co-domain
Where, domain of
Onto function defined as every element in the co-domain has at least one pre image in the domain of function.
Here, we need to give an example of a function for one-one but not onto.
Let we consider the function,
, given by
Let us consider two elements and in the domain of f, so we get
Now we know the condition for finding a one-one function.
Hence, the function is one-one.
Now, we need to proveis not onto
Let , such that x,
If we put
, which is cannot be true as supposed in solution.
Hence, the given function is not onto.
So, is an example of one-one but not onto function.