NDA 2025
- Exam
- NDA
- Year
- 2025
- Subject
- Mathematics
- Chapter
- Functions
NDA 2025 · Mathematics · Functions
Consider the following for the two (02) items that follow: Let f =...
Consider the following for the two (02) items that follow:
Let .
Consider the following statements:
I. is one-one function.
II. is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?
Let .
Consider the following statements:
I. is one-one function.
II. is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?
Options
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Correct answer
A. I only
Step-by-step solution
The given function is .
The domain of is and the range of is .
Since each element in the domain has a distinct image in the range, is a one-one function. Statement I is correct.
If the codomain is the set of natural numbers, the range is a proper subset of the codomain. Since the range is not equal to the codomain, is not an onto function. Statement II is incorrect.
Therefore, only Statement I is correct.
Answer: I only
The domain of is and the range of is .
Since each element in the domain has a distinct image in the range, is a one-one function. Statement I is correct.
If the codomain is the set of natural numbers, the range is a proper subset of the codomain. Since the range is not equal to the codomain, is not an onto function. Statement II is incorrect.
Therefore, only Statement I is correct.
Answer: I only