Answer to Question #349855 in Discrete Mathematics for mengal

Question

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.

Answer 1

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

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

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

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

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

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

It shows that $f$ is a mapping from A to B.