Answer to Question #245517 in Discrete Mathematics for Alina

Question

Consider the following functions and determine if they are bijective. [A function is said to be bijective or bijection, if a function f : A → B is both one-to-one and onto.]

f : R × R → R, f(n, m) = 2m − n

Answer 1

One-to-one function is a function f that maps distinct elements to distinct elements.

Onto function is a function f that maps an element x to every element y.

The given function is not one-to-one: for example: $f(3,2)=1=f(1,1)$

So, the function is not bijective.