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The statement is **True**.

Here’s why: If a function \( F \) is invertible, it must be both **bijective**, meaning it is both injective (one-to-one) and surjective (onto). When a function is bijective, its inverse \( F^{-1} \) also has these properties but with respect to the domains and codomains reversed. Therefore, if \( F \) is invertible, then \( F^{-1} \) is also bijective, making it **surjective** on its respective domain.

Would you like further explanation or examples?

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Here are 5 related questions to deepen understanding:
1. What is the difference between injective, surjective, and bijective functions?
2. Can a function be invertible if it is only injective but not surjective?
3. How do you determine if a given function has an inverse?
4. Why does a bijective function imply that both the function and its inverse are surjective?
5. What are some real-world examples of bijective functions?

**Tip:** Remember, if a function is invertible, it must be both one-to-one (injective) and onto (surjective), ensuring its inverse is also a valid function.

If a function F is invertible, then its inverse, F^{-1}, is surjective. True or False?

Explore why an invertible function implies that its inverse is surjective. This question examines key mathematical concepts like invertibility, bijectivity, and the properties of inverse functions. Suitable for advanced high school or introductory college-level students.

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