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function f: X -> Y is called:
- bijection each element of X is paired with exactly one element of Y, and each element of Y is paired with exactly one element of X.
a) f (x) = 3x – 1
Since this function is defined for every continious and monotonically increasing, than for any X it has different f(x), which means it is one-to-one. Lets put , which means it is not onto.
This function is one-to-one and not onto
b) f(x) = x2 + 2x + 1
Since for f(x) = 1 both x = 0 and x = -2 are fit, than f(x) is not one-to-one. Also for f(x) = -1 we have
x2 + 2x + 2 = 0 , which means there is no such
So, this function is neither onto nor onto.
c) f(x,y)= 2y -3x
Since for f(x,y) = -1 both x = 1, y = 1 and x = -1, y = -2 are fit, then f(x,y) is not one-to-one.
Let . Then we can put x = a and receive y = 2a. , which means f(x, y) is onto
This function is onto and not one-to-one