How to prove injection and surjection for a function with 2 variables?

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To prove injection and surjection for a function with two variables, the approach is similar to that for a single variable. An example function is f: R x R → R defined by f(x, y) = x + y. This function is not injective, as demonstrated by f(1, 0) = f(0, 1). However, it is surjective because for any real number a, there exists a pair (a, 0) such that f(a, 0) = a. Understanding these properties is crucial for analyzing functions of multiple variables.
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how do you prove injection and surjection of the function of 2 variables. for example f:RxR->R
 
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The same way you prove it for 1 variable.
Can you give us a specific map?
 
For example the map f:RxR--> R:x-->x+y.

This is not an injection, since f(1,0)=f(0,1).
This is a surjection. Take a in R, then f(a,0)=a.
 

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