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pmooney12
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how do you prove injection and surjection of the function of 2 variables. for example f:RxR->R
An injection is a function that maps each element of its domain to a unique element in its range. In other words, no two elements in the domain can map to the same element in the range. This is also known as a one-to-one function.
A surjection is a function that maps each element of its domain to at least one element in its range. In other words, every element in the range has at least one corresponding element in the domain. This is also known as an onto function.
The main difference between an injection and a surjection is that an injection maps each element of its domain to a unique element in its range, while a surjection maps each element of its domain to at least one element in its range. In other words, an injection has no repeated outputs, while a surjection may have repeated outputs.
Yes, a function can be both an injection and a surjection. This type of function is called a bijection. It maps each element of its domain to a unique element in its range and also maps each element of its domain to at least one element in its range.
To determine if a function is an injection, you can use the horizontal line test. If a horizontal line can intersect the function's graph at most once, then the function is an injection. To determine if a function is a surjection, you can use the vertical line test. If a vertical line can intersect the function's graph at least once, then the function is a surjection.