Answer to Question #349855 in Discrete Mathematics for mengal

Question #349855

Let A = {1, 2, 3, 4} and B = {0, 3, 6, 8, 12, 15}. Consider a rule f (x) = x² - 1, x∈A, then show that f is a mapping from A to B.



1
Expert's answer
2022-06-13T23:23:49-0400

Let's consider a rule f(x)=x²1,xAf (x) = x² - 1, x∈A and find an image of every element in A.

At x=1:x=1: f(1)=121=0B.f(1)=1^2-1=0\in B.

At x=2:f(2)=221=41=3B.x=2: \: f(2)=2^2-1=4-1=3\in B.

At x=3:f(3)=321=91=8B.x=3: \: f(3)=3^2-1=9-1=8\in B.

At x=4:f(4)=421=161=15B.x=4: \: f(4)=4^2-1=16-1=15\in B.


We see that every element xAx∈A has an image f(x)Bf(x)∈B and the image is unique.

It shows that ff is a mapping from A to B.


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