Let X 2101 and Y 2101 Define a function F X rightarrow Y a

Let X = {-2,-1,0,1} and Y = {-2,-1,0,1}. Define a function F: X rightarrow Y as follows: F(x) = x^2 + x - 1. Prove that F is neither 1-1 nor onto.

Solution

For a one-one function, each element in its co-domain must have only one pre-image in its domain. So, F(x) is not one-one because F(-2)=F(1) and F(-1)=F(0)
For an onto function, the range of the function must be equal to its co-domain. F(x) is not onto because the range of F(x) has only the values {-1,1} where as its co-domain is {-2,-1,0,1}.

x	F(x)=x2+x-1
-2	1
-1	-1
0	-1
1	1