Which characteristic is unique to an injective function?

Which characteristic is unique to an injective function?

• A. It has at least one output that corresponds to multiple inputs
• B. It can be both injective and surjective
• C. Each output is the result of exactly one input
• D. It does not have a defined range

Answer: (C)

An injective function, also known as a one-to-one function, possesses the unique characteristic that each element in the function's domain maps to a distinct element in its codomain. This implies that for every output, there is exactly one input that produces it, meaning no two different inputs can generate the same output. This is fundamental to understanding how injective functions operate—ensuring uniqueness in mapping is what sets them apart. The other options do not accurately reflect the defining traits of an injective function. While injective functions can exist in various contexts, such as also being part of a bijective function when they are also surjective, the core characteristic of being one-to-one remains the distinguishing feature. Similarly, a valid injective function does have a defined range—it merely may not use every possible value in the codomain, but there are no outputs that correspond to multiple inputs.

An injective function, also known as a one-to-one function, possesses the unique characteristic that each element in the function's domain maps to a distinct element in its codomain. This implies that for every output, there is exactly one input that produces it, meaning no two different inputs can generate the same output. This is fundamental to understanding how injective functions operate—ensuring uniqueness in mapping is what sets them apart.

The other options do not accurately reflect the defining traits of an injective function. While injective functions can exist in various contexts, such as also being part of a bijective function when they are also surjective, the core characteristic of being one-to-one remains the distinguishing feature. Similarly, a valid injective function does have a defined range—it merely may not use every possible value in the codomain, but there are no outputs that correspond to multiple inputs.