Function is bijective when it is:
A function is bijective when it is:
- A.
Neither injective nor surjective
- B.
Injective but not surjective
- C.
Surjective but not injective
- D.
Both injective and surjective
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Correct answer: D
A bijective function is a function that is both injective (one-to-one) and surjective (onto).
Injective (one-to-one): different inputs give different outputs; no two distinct domain elements share the same image.
Surjective (onto): every element of the codomain is the image of at least one element from the domain.
Consequence: a bijective function has an inverse function that reverses the mapping from codomain back to domain.
Examples:
f(x) = x on the real numbers is bijective: it is both one-to-one and onto.
f(x) = x² on the real numbers is not bijective: it is not injective (x and -x map to the same value) and not surjective onto all real numbers (negative numbers have no preimage).