Functions

Step 1: Understanding one-one function.
A function is one-one (or injective) if distinct elements in the domain map to distinct elements in the codomain . That is, if , then .

Step 2: Check the given function.
The function is given by: We observe that: - - - There is no repetition of values in the range (i.e., 4, 5, and 6 are distinct). Therefore, is one-one.

Step 3: Conclusion.
Since all elements of map to distinct elements in , the function is one-one.

Step 1: Understanding the onto function.
A function is said to be onto (or surjective) if every element in the codomain has a corresponding element in the domain . In other words, the range of the function is equal to the entire codomain.

Step 2: Conclusion.
Since is an onto function, the range of is equal to the codomain . Therefore, the statement is true.

Step 1: Understand the function.
The given function is . This is a linear function, and a linear function is always one-to-one (bijective) if the coefficient of is non-zero.

Step 2: Conclusion.
Since the function is both one-to-one and onto, the correct answer is option (1).