Every injective function is invertible.Group startsTrue or FalseTrue, unselectedFalse, unselected
Question
Every injective function is invertible.
Group starts
True or False
- True, unselected
- False, unselected
Solution
To determine whether the statement "Every injective function is invertible" is true or false, we need to analyze the given information.
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The statement claims that every injective function is invertible.
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An injective function is a function where each element in the domain maps to a unique element in the codomain. In other words, no two different elements in the domain can map to the same element in the codomain.
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An invertible function is a function that has an inverse function. An inverse function undoes the mapping of the original function, meaning that applying the inverse function to the output of the original function will give the original input.
Based on this information, we can conclude that the statement is false. Not every injective function is invertible. While injective functions guarantee that each element in the domain maps to a unique element in the codomain, it does not necessarily mean that there exists an inverse function that can undo the mapping.
Therefore, the correct answer is False.
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