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markosheehan
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is the function x³-5x²+3x+5 injective. how can you tell
To determine if a function is injective, you can use the "horizontal line test". This involves drawing a horizontal line anywhere on the graph of the function. If the line intersects the graph at more than one point, then the function is not injective. If the line only intersects the graph at one point, then the function is injective.
An injective function is one in which each element in the domain maps to a unique element in the range. In other words, no two elements in the domain can map to the same element in the range.
Yes, a function can be both injective and surjective. This type of function is called a bijective function. In a bijective function, every element in the domain maps to a unique element in the range, and every element in the range has a corresponding element in the domain.
To prove that a function is injective, you can use the definition of an injective function. You can show that no two elements in the domain map to the same element in the range, or you can use a more mathematical approach such as a proof by contradiction.
There is no difference between a one-to-one function and an injective function. They both refer to the same concept of a function where each element in the domain maps to a unique element in the range. The terms are simply used interchangeably in different contexts.