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A function is invertible if it isa) surjectiveb) bijectivec) injectived) neither surjective nor injective
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Q. A function is invertible if it isa) surjectiveb) bijectivec) injectived) neither surjective nor injective
- Function Invertibility Definition: A function is invertible if it has a unique output for every input and a unique input for every output. This means that the function must be both injective (one-to-one) and surjective (onto). A function that is both injective and surjective is called bijective.
- Options Analysis: To determine which option corresponds to a function being both injective and surjective, we look at the options provided:a) surjective - This means the function is onto, but does not guarantee it is one-to-one.b) bijective - This means the function is both onto and one-to-one.c) injective - This means the function is one-to-one, but does not guarantee it is onto.d) neither surjective nor injective - This means the function is neither onto nor one-to-one, so it cannot be invertible.
- Correct Answer: Based on the definitions, the correct answer is that a function must be bijective to be invertible. Therefore, the correct option is bijective.
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