Functions

Step 1: Understanding one-to-one (injective) functions. A function is one-to-one (injective) if:

Step 2: Checking injectivity of . Given: Let : Canceling from both sides: Taking the cube root: Since the function satisfies the condition for injectivity, it is one-to-one.

Step 3: Checking onto (surjective) property. For surjectivity, must cover all integers. Since cube functions do not necessarily map to all integers, is not necessarily onto over .

Conclusion: The function is one-to-one.